Question

What value or values of x satisfy 2|x+5.3|=4.2

a. x can only equal –3.2.
b. x can only equal 7.4.
c. x can equal –3.2 or –7.4.
d. x can equal –3.2 or 7.4.

Answer 1

We have, /x+5.3/ = 2.1;
Then, x + 5.3 = 2.1 or x + 5.3 = -2.1;
x = 2.1 - 5.3; x = -3.2;
x = -2.1-5.3; x = -7.4;
The correct answer is c.

Answer 2

we have

`2\left|x+5.3\right|=4.2`

Step 1

Find the first solution (case positive)

`2(x+5.3)=4.2`

Eliminate the parenthesis left side

`2x+10.6=4.2`

Subtract
`10.6` both sides

`2x=4.2-10.6`

`2x=-6.4`

Divide by
`2` both sides

`x=-3.2`

Step 2

Find the second solution (case negative)

`2[-(x+5.3)]=4.2`

Eliminate the parenthesis left side

`-2x-10.6=4.2`

Adds
`10.6` both sides

`-2x=4.2+10.6`

`-2x=14.8`

Divide by
`-2` both sides

`x=-7.4`

therefore

the answer is the option C

x can equal –3.2 or –7.4