Question

PLEASE HELP WITH THIS ILL GIVE BRAINLIEST

Answer 1

Answer:

$\text{a. }x=7, x=-7, \\\text{b. }x=16, x=-16, \\\text{c. }x=3, x=-17, \\\text{d. }x=7, x=-7$

Step-by-step explanation:

For $|x|=y$, we have two cases:

$\begin{cases}x=y, \\x=-y\end{cases}$

Using this, we can solve all four of the problems:

$\text{a. }|x|=7,\\\begin{cases}x=7, \\x=-7\end{cases}$

$\text{b. }|2x|=32,\\\begin{cases}x=16, \\x=-16\end{cases}$

$\text{c. }|x+7|=10,\\\begin{cases}x+7=10, x=\boxed{3,} \\x+7=-10, x=\boxed{-17}\end{cases}$

$\text{d. }5|x|=35,\\\begin{cases}x=7, \\x=-7\end{cases}$

Answer 2

Answer:

a) x = 7, x = - 7

b) x = 16, x = - 16

c) x = 3, x = - 17

d) x = 7, x = - 7

Step-by-step explanation:

When you have absolute value on a variable, the variable has two results.

Example:

lxl = 2

x = 2, or x = - 2

a. lxl = 7

x = 7, x = - 7

b. l2xl = 32

l2xl ÷ 2 = 32 ÷ 2

lxl = 16

x = 16, x = - 16

c. lx + 7l = 10

x + 7 = 10

x + 7 = - 10

x + 7 = 10

x + 7 - 7 = 10 - 7

x = 3

x + 7 = - 10

x + 7 - 7 = - 10 - 7

x = - 17

d. 5lxl = 35

5x = 35

5x = - 35

5x = 35

5x ÷ 5 = 35 ÷ 5

x = 7

5x = - 35

5x ÷ 5 = - 35 ÷ 5

x = - 7