Question

Solve the inequality.

2(4+2x)≥5x+5


Show your steps please.

Answer 1

x≤3

Explanation:

2(4+2x)≥5x+5

Step 1: Simplify both sides of the inequality.

4x+8≥5x+5

Step 2: Subtract 5x from both sides.

4x+8−5x≥5x+5−5x

−x+8≥5

Step 3: Subtract 8 from both sides.

−x+8−8≥5−8

−x≥−3

Step 4: Divide both sides by -1.

−x−1≥−3−1

x≤3

Answer 2

`x\leq 3`

Explanation:

So we have the inequality:

`2(4+2x)\geq 5x+5`

First, let's distribute the left side:

`2(4)+2(2x)\geq 5x+5`

Multiply:

`8+4x\geq5x+5`

Now, let's isolate the x-variable. Subtract 8 from both sides:

`(8+4x)-8\geq (5x+5)-8`

The left side cancels. Subtract on the right:

`4x\geq 5x-3`

Now, let's subtract 5x from both sides:

`(4x)-5x\geq (5x-3)-5x`

The right side cancels. Subtract on the left:

`-x\geq -3`

Now, let's multiply both sides by -1.

Since we're multiplying by a negative, we flip the sign. So:

`-1(-x)\leq (-1)(-3)`

Multiply:

`x\leq 3`

So, our solution is all numbers less than or equal to 3.

And we're done!