Answer:
Last option; x = 1 or x = -5
Step-by-step explanation:
1. Simplify the equation.
Step 1: Add 7 to both sides.
- [tex]4(|2x+4|)-7+7=17+7[/tex]
- [tex]4(|2x+4|) = 24[/tex]
Step 2: Divide both sides by 4.
- [tex]\frac{4(|2x+4|)}{4} = \frac{24}{4}[/tex]
- [tex]|2x+4| = 6[/tex]
2. Now that we simplified the equation to this, we have to solve for absolute value. We know either [tex]2x + 4 = 6[/tex] or [tex]2x + 4 = -6[/tex].
3. (Solving for 1st possibility)
Step 1: Subtract 4 from both sides.
- [tex]2x + 4 - 4 = 6-4[/tex]
- [tex]2x = 2[/tex]
Step 2: Divide both sides by 2.
- [tex]\frac{2x}{2} = \frac{2}{2}[/tex]
- [tex]x = 1[/tex]
4. (Solving for 2nd possibility)
Step 1: Subtract 4 from both sides.
- [tex]2x+4-4=-6-4[/tex]
- [tex]2x = -10[/tex]
Step 2: Divide both sides by 2.
- [tex]\frac{2x}{2}= \frac{-10}{2}[/tex]
- [tex]x = -5[/tex]
5. Now that we have the outcomes of both of our possibilities as x = 1 or x = -5, the last option matches with what we got.
