Question

Solve 4(5x+7)≤13 . Write the solution in set builder notation.

example of set builder notation: x

Answer 1

`\left\x`

Explanation:

Given inequality:

`4(5x+7)\leq13`

Divide both sides by 4:

`\implies (4(5x+7))/(4)\leq(13)/(4)`

`\implies 5x+7\leq (13)/(4)`

Subtract 7 from both sides:

`\implies 5x+7-7\leq (13)/(4)-7`

`\implies 5x\leq (13)/(4)-(28)/(4)`

`\implies 5x\leq -(15)/(4)`

Divide both sides by 5:

`\implies (5x)/(5)\leq (-(15)/(4))/(5)`

`\implies (5x)/(5)\leq -(15)/(4)* (1)/(5)`

`\implies x\leq -(15)/(20)`

`\implies x \leq -(3)/(4)`

Therefore, the solution in set builder notation is:

`\left\x\leq-(3)/(4)\right\`