Question

please help! ill give brainlyest! solve the absolute value equation

Answer 1

Answer:

x = $\frac{40}{9}$ , x = - $\frac{56}{9}$

Step-by-step explanation:

Given

$\frac{1}{2}$ | $\frac{3}{4}$ x + $\frac{2}{3}$ | - 1 = 1 ( add 1 to both sides )

$\frac{1}{2}$ | $\frac{3}{4}$ x + $\frac{2}{3}$ | = 2 ( divide both sides by $\frac{1}{2}$ )

| $\frac{3}{4}$ x + $\frac{2}{3}$ | = 4

The absolute value always gives a positive result, however, the expression inside can be positive or negative, then

$\frac{3}{4}$ x + $\frac{2}{3}$ = 4 ( multiply through by 12 to clear the fractions )

9x + 8 = 48 ( subtract 8 from both sides )

9x = 40 ( divide both sides by 9 )

x = $\frac{40}{9}$

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OR

- ($\frac{3}{4}$ x + $\frac{2}{3}$ ) = 4 , distribute left side

- $\frac{3}{4}$ x - $\frac{2}{3}$ = 4 ( multiply through by 12 to clear the fractions )

- 9x - 8 = 48 ( add 8 to both sides )

- 9x = 56 ( divide both sides by - 9 )

x = $\frac{56}{-9}$ = - $\frac{56}{9}$

Answer 2

1/2丨3/4x＋2/3丨－1＝1

丨3/4x＋2/3丨－2＝2

丨3/4x＋2/3丨＝2＋2

丨3/4x＋2/3丨＝4

3/4x＋2/3＝4
3/4x＋2/3＝－4

x＝40/9
x＝－56/9

Hope my answer helped u :)