The general steps of solving a univariate inequality are summarized and compared with solving a univ

Basic steps: 1) If there is a fraction, multiply a number on both sides of the inequality at the same time, remove the denominator, and make the inequality all integers. (There are decimal places that are the same).

2) Move items, move the unknown to one side and the known to the other;

3) Merge similar terms, perform four operations on the unknown number, and also perform the operation of the known number on the other side;

4) Finally, an unknown number with coefficients is equal to a known number;

5) Divide the coefficient by the unknown at the same time.

Note: (very important, also the difference between equations and inequalities):

In an inequality, when both sides of the inequality are multiplied or divided by a negative number at the same time, the inequality is changed (greater than becomes less than, less than becomes greater than), but there is no such sign in the equation.

A: 1Go to the denominator, 2Remove the brackets, 3Shift, 4Merge the same kind of items, 5The coefficient is 1

The steps for solving a unary inequality are essentially the same as for solving a unitary equation, with the only difference being that when both sides of the inequality are multiplied (or divided) by a negative number, the inequality sign is redirected.

1.remove the denominator (if there is one);

2.remove parentheses (if there are parentheses);

3.Move items (note the change of signs);

4.Merge terms of the same kind (as in equations);

5.coefficients to one (note the "<

", the symbol changes);

In fact, it's not difficult, as long as you find a good relationship between equal quantities, like 2+x=3 can be said to be 3-2=x, which is equivalent to the sum of elementary schools, adding or something, just find a good relationship, in fact, it is evolved from the equivalence formula.

Remove the denominator and remove the parentheses.

Move items merge items of the same kind.

The coefficient is 1

The general steps to solve a unary inequality are: remove the denominator of the loose sail; remove parentheses; Transposition; merging similar items; The coefficient is 1where when the coefficient is negative, the direction of the unequal sign is changed.

The general steps to solve a unary inequality are as follows: remove the denominator, remove the parentheses, shift the terms, merge the similar terms, and reduce the coefficient to 1;

When the coefficient is negative, the direction of the unequal sign is changed

General steps to solve a unary primary inequality Remove the denominator (according to the properties of inequalities 2 or 3) Remove the parentheses (according to the law of deparentheses, the multiplicative distributive law) Shift terms (according to the properties of the inequality 1) Merge the same terms (according to the law of merging the same terms).

Thank you for adopting!

1. Remove the denominator (the nature of inequality - the left and right sides of the inequality are multiplied or divided by the same positive number at the same time, and the direction of the inequality sign does not change, and the direction of the inequality sign changes when the left and right sides of the inequality are multiplied or divided by the same negative number at the same time).

2. De-parentheses (the nature of integers - the law of de-parentheses).

3. Shift term (the property of inequality - the left and right sides of the inequality add or subtract the same number at the same time, and the direction of the inequality sign is not on the side).

4. Merge similar terms (the property of the integer - the coefficient is added, and the letter part is unchanged) 5. The coefficient is turned into one (the property of the inequality - the left and right sides of the inequality are multiplied or divided by the same positive number at the same time, and the direction of the inequality sign is unchanged, and the left and right sides of the inequality are multiplied or divided by the same negative number at the same time, and the direction of the inequality sign changes).

The solution to the unary inequality is based on the property of the inequality1: both sides of the inequality are added (or subtracted) to the same integer manuscript, and the direction of the inequality sign remains the same. Inequality property 2:

Both keys of the inequality are multiplied (or divided) by the same positive number, and the direction of the unequal sign is in the same direction. Inequality property 3: Both sides of the inequality are multiplied (or divided) by the same negative number, and the direction of the inequality sign is reversed.

Same: are all solutions to find unknowns, the methods are shifting, removing the denominator, multiplication, division, addition, and subtraction

1. The number of solutions is different.

Unary equations generally have one solution, and inequalities are a set of solutions.

2. The symbols are different, and the equation is a "=" sign.

The inequalities are, , etc.

3. Multiply and divide by a number or algebraic formula that is not 0 on both sides of the equation at the same time, it is always a "=" sign and an inequality sign should change the direction of the unequal sign (except for the ≠ sign).

Unary Linear Equations.

1) Both sides of the equation must participate in the operation, and it is the same operation (to add and multiply).

2) The number added (or subtracted) or multiplied (or divided) on both sides of the equation must be the same number.

3) Since 0 cannot be used as a divisor or denominator, the divisor cannot be 0 when both sides of the equation are divided by the same number.

Unary one-time inequality.

The formula that uses " " or " " to express the relationship between size and size is called an inequality; The formula that uses "≠" to represent an inequality relationship is also an inequality. Inequalities that are similar to unary equations, with an unknown number and the number of unknowns being 1, are called unary inequalities.

Similarities: (1) The unary inequality is exactly the same as the solution of the unary equation, that is: remove the denominator; remove parentheses; Transposition; merging similar items; Coefficients to 1 (2) have unknowns.

Differences: (1) When solving the inequality, in steps and , if the multiplier or divisor is negative, change the direction of the inequality sign. (2) The symbols are different.

The unary inequality is solved in exactly the same way as the unary equation, i.e.: remove the denominator; remove parentheses; Transposition; merging similar items; The coefficient is 1The difference is that when solving an inequality, step and , if the multiplier or divisor is negative, change the direction of the inequality sign...

The difference is the degree of reaction...

1. The similarities and differences between the concepts of unary inequalities and unary equations are similar: both contain only one unknown, the number of unknowns is 1, and both left and right sides are integers

Differences: Unary Inequalities represent inequalities, and unary equations represent equality Relations (3) Similar to equations, we call or call the standard form of unary inequalities 2. Similarities and differences between unary inequalities and solutions to unary equations: the steps are the same, both are deformed, turning the left side into and the right side into a constant Differences:

In step (1) to remove the denominator and step (5) to change the coefficient of the term to 1, it is necessary to decide whether to change the direction of the unequal sign according to the positive or negative of the number of the same multiplication (or division).

Note: (1) The shift-term rule for solving equations is also applicable to solving inequalities (2) When solving inequalities, the above five steps may not be used, and they may not be in the order of top to hundred, and the solution steps should be flexibly arranged according to the form of inequalities After being proficient, the steps and tests can also be combined and simplified

1.remove the denominator (if there is one);

2.remove parentheses (if there are parentheses);

3.Move items (note the change of signs);

4.Merge terms of the same kind (as in equations);

5.coefficient to one (note the change in the sign of "<);

1.The main types of inequalities and inequalities are multiple-choice questions, fill-in-the-blank questions, calculation questions, and solution questions. 2.

The main knowledge points examined in the content of inequalities and inequality groups are: the basic properties of inequalities, the solution set of solving a unary one-time inequality and representing the inequality on the number line, solving an inequality group composed of two unary one-dimensional inequalities and using the number line to determine the solution set, and the simple application of inequality and inequality groups.

2: 1.The main knowledge points examined in this part of equations and inequalities are:

According to the quantitative relationship in the specific problem, the equation is listed, solved and tested, the solution of the equation can be estimated, the solution of the equation can be solved, the solution of the unary linear equation, the simple system of binary linear equations, the fractional equation that can be reduced to the unary linear equation, the unary quadratic equation with simple coefficients, the meaning and basic properties of the inequality, the solution of the unary inequality and the representation of the solution set on the number line, the solution of the unary linear inequality and the use of the number line to determine the solution set of the inequality group, and the solution of the simple application problem.

1.Solve solutions in groups of inequalities separately.

2.Then find the same range of solutions for these inequalities.

General steps to solve the equation:1Move the term with unknowns to the left of the inequality and the constant term to the right.

2.The coefficients of the unknowns are divided by both sides at the same time, and the sign transformation is as follows:

1) When the coefficient of unknown numbers is positive, the number does not change after not being marked.

2) When the coefficient of the unknown number is negative, the change sign after the division, " and ", > and <, mutual change.

The general steps of solving the equation, 1, shift the term, is to move the constant term to the right, 2The difference between the two sides is that the coefficient of the unknown term is divided by the same elementary inequality operation.

However, if the coefficient of the unknown term is negative, the sign and direction should be changed.