SOLUTION: Use the properties of inequalities to solve the inequality. Write the solution set using set-builder notation. &#8722;3(x + 2) &#8804; 5x + 7 {x| }

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Question 1131538: Use the properties of inequalities to solve the inequality. Write the solution set using set-builder notation.
−3(x + 2) ≤ 5x + 7
{x| }

Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Given inequality

Distribute

Multiply

Add 3x to both sides

Combine like terms

Subtract 7 from both sides

Combine like terms

Flip the sides of the inequality

Divide both sides by 8 to isolate x

Simplify

The answer is the set of all x values such that x is equal to -13/8 or it is larger than this value

We write that answer in set-builder notation like so

note: The fancy R means "the set of real numbers". So saying means x is in the set of real numbers

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
−3(x + 2) ≤ 5x + 7
-3x - 6 <= 5x + 7
0 <= 8x + 13
8x + 13 >= 0
8x >= -13
x >= -13/8
Use whatever notation you like.

SOLUTION: Use the properties of inequalities to solve the inequality. Write the solution set using set-builder notation. &#8722;3(x + 2) &#8804; 5x + 7 {x| }

SOLUTION: Use the properties of inequalities to solve the inequality. Write the solution set using set-builder notation. −3(x + 2) ≤ 5x + 7 {x| }