Math  /  Algebra

Question3) Solve the inequality. Use a calculator as needed. 9x4(x+7)<429 x-4(x+7)<-42 x>2.8x>-2.8 x1x \leq-1 x<2.8x<-2.8 x<2.8x<2.8

Studdy Solution

STEP 1

1. The inequality 9x4(x+7)<429x - 4(x + 7) < -42 involves basic algebraic manipulations.
2. Simplification of the inequality will help isolate the variable xx.
3. The solution should identify the correct range of values for xx that satisfy the inequality.

STEP 2

1. Distribute and simplify the terms within the inequality.
2. Combine like terms to isolate the variable xx.
3. Solve the simplified inequality for xx.
4. Check the solution against the given options to find the correct range.

STEP 3

Distribute 4 -4 inside the parentheses in the inequality 9x4(x+7)<42 9x - 4(x + 7) < -42 .
9x4x28<42 9x - 4x - 28 < -42

STEP 4

Combine like terms involving xx.
(9x4x)28<42 (9x - 4x) - 28 < -42 5x28<42 5x - 28 < -42

STEP 5

Add 2828 to both sides of the inequality to isolate the term involving xx.
5x28+28<42+28 5x - 28 + 28 < -42 + 28 5x<14 5x < -14

STEP 6

Divide both sides of the inequality by 55 to solve for xx.
x<145 x < \frac{-14}{5} x<2.8 x < -2.8

STEP 7

Compare the solution x<2.8x < -2.8 with the given options to determine the correct range.
The correct option is: x<2.8 x < -2.8
Solution: The inequality 9x4(x+7)<429x - 4(x + 7) < -42 simplifies to x<2.8x < -2.8.

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