Question

1. solve the multi - step equation: 3(2x - 4) - 5x = - 7

a. x = 5
b. x = - 1
c. x = 3
d. x = - 5

1. solve the multi - step equation: 4(3x + 2) - 7x = 3x + 20

a. x = 4
b. x = 5
c. x = 6
d. x = 1

1. jim is building a right triangle flower bed. one of the acute angles is 75 degrees. what is the measure of the other acute angle?

a. 30°
b. 25°
c. 20°
d. 15°

Explanation:

Question 14

Step1: Distribute the 3

$3(2x - 4) - 5x = -7$ becomes $6x - 12 - 5x = -7$

Step2: Combine like terms

$6x - 5x - 12 = -7$ simplifies to $x - 12 = -7$

Step3: Solve for x

Add 12 to both sides: $x - 12 + 12 = -7 + 12$ which gives $x = 5$

Step1: Distribute the 4

$4(3x + 2) - 7x = 3x + 20$ becomes $12x + 8 - 7x = 3x + 20$

Step2: Combine like terms

$12x - 7x + 8 = 3x + 20$ simplifies to $5x + 8 = 3x + 20$

Step3: Subtract 3x from both sides

$5x - 3x + 8 = 3x - 3x + 20$ gives $2x + 8 = 20$

Step4: Subtract 8 from both sides

$2x + 8 - 8 = 20 - 8$ gives $2x = 12$

Step5: Divide by 2

$\frac{2x}{2} = \frac{12}{2}$ so $x = 6$ (Wait, there's a mistake in the original handwritten work. Let's correct it. After step 2: $5x + 8 = 3x + 20$, subtract 3x: $2x + 8 = 20$, subtract 8: $2x = 12$, divide by 2: $x = 6$. But the original handwritten had an error. However, following the correct steps: )
Wait, let's redo:

1. Distribute: $12x + 8 - 7x = 3x + 20$
2. Combine like terms: $5x + 8 = 3x + 20$
3. Subtract 3x: $2x + 8 = 20$
4. Subtract 8: $2x = 12$
5. Divide by 2: $x = 6$

But the options have C as x=6. Wait, the original handwritten had a mistake in combining terms (wrote 8x instead of 5x - 3x = 2x). So the correct answer is C. x=6.

In a right triangle, the sum of angles is $180^\circ$. One angle is $90^\circ$ (right angle), one is $75^\circ$, so the other acute angle $x$ satisfies $90 + 75 + x = 180$.

Step1: Simplify left side

$165 + x = 180$

Step2: Subtract 165

$x = 180 - 165 = 15^\circ$

Answer:

A. x = 5

Question 15