How to find the solution to an inequality with subtraction

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Algebra › How to find the solution to an inequality with subtraction

Questions 1 - 10

1

What is a possible valid value of ?

Explanation

This inequality can be rewritten as:

4_x_ + 14 > 30 OR 4_x_ + 14 < –30

Solve each for x:

4_x_ + 14 > 30; 4_x_ > 16; x > 4

4_x_ + 14 < –30; 4_x_ < –44; x < –11

Therefore, anything between –11 and 4 (inclusive) will not work. Hence, the answer is 7.

2

Solve for .

$5 + 3p \leq 2p + 12$

$p\leq 7$

$p\leq \frac{19}{5}$

$p\leq-7$

$p\leq17$

$p\leq\frac{7}{5}$

Explanation

First subtract 2p from both sides:

p + 5 < 12.

Then subtract 5 from both sides:

p < 7

3

Solve the inequality:

$x\leq-1$

Explanation

Group the integers on the left side and the values on the right side.

Subtract three on both sides.

Simplify both sides.

Subtract on both sides.

Simplify both sides.

The answer is:

4

Solve the inequality: $x+6\leq -30$

$x\leq -36$

$x\geq36$

$x\geq-36$

Explanation

Solve this inequality by subtracting six from both sides. This will isolate the x-variable.

$x+6-6\leq -30-6$

Simplify both sides. A negative number subtracting a number will be further way from zero.

The answer is: $x\leq -36$

5

Solve the inequality:

$\small x+12>4+3$

$\small x>-5$

$\small x>19$

$\small x<5$

$\small x<-19$

$\small x>11$

Explanation

First combine like terms on the right side of the inequality to obtain $\small x+12>7$ . Next, try to isolate the variable: $\small x+12\mathbf{-12} >7\mathbf{-12}$ .

The answer is therefore $\small x>-5$ .

6

Solve the following inequality:

Explanation

In order to isolate the variable, we will need to subtract 10 on both sides of the equation.

Simplify the left and the right side of the equation.

The answer is:

7

$\left | 4x+4 \right |< 20$

Which one of the following is is a valid value for ?

Explanation

Since the inequality includes absolute value, you have two possiblities to consider: when the outcome is positive and when it is negative. When you consider the negative outcome, you must flip the inequality sign to solve for :

This means that is less than positive 20 AND greater than negative 20:

AND

For each case, you will first subtract 4 from the left to the right. Then, you will divide both sides by 4 to isolate :

AND

AND

This gives you the interval for valid values of :

8

Solve the following inequality:

$x\leq-84$

Explanation

Subtract nine on both sides.

Simplify both sides.

The answer is:

9

Solve the inequality:

Explanation

Group the integers and the terms with the x-variables.

Subtract six from both sides.

Simplify both sides.

Subtract from both sides.

Simplify both sides.

We can rewrite this inequality.

The answer is:

10

Solve the following inequality: $x+7\leq -21$

$x\leq -28$

$x\leq -14$

$x\geq -28$

Explanation

In order to isolate the variable, subtract 7 from both sides of the inequality.

$x+7-7\leq -21-7$

Simplify both sides.

$x\leq -28$

The answer is: $x\leq -28$

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