Which of the following is the value of x in the equation below.

(|2x - 4| - 10 = 2)

1. Add 13 to both sides to isolate the absolute value term, resulting in\(\left|3x - 7 \right| = 15\)

2. Consider two cases:

   • When (+(3x-7))is positive, solve for x to get (3x = 15 + 7) then \(3x = 22 \quad \text{finally} \quad x = \frac{22}{3}\)
   • When (-(3x-7)) is negative (but the absolute value makes it positive). Solve for x to get (-3x = 15 - 7) then\(-3x = 8 \quad \text{finally} \quad x = -\frac{8}{3}\)

So, there are two possible solutions: \(x = \frac{22}{3} \quad \text{or} \quad x = -\frac{8}{3}\)

The question requires us we make x the subject of the formula.

First, we subtract rw to both sides of the equation

Multiply both sides by y

Thus, the formula for finding the value of x is y(z-rw).

We are asked to form an equation to find Joe’s uncle’s age to the age of Joe.

First, we find Joe’s age which is k. We know that Joe’s uncle’s age is four times that of Joe less 8. Then,

Joe’s uncle’s age, u = 4k-8.

Thus, the age of Joe’s uncle is u=4k-8.

Explanation:

We need to find the value of x from the given equation. First, we move the value of 10 to the right-hand side of the equation.

Add 10 to both sides of the equation

Next, we apply the absolute rule:

If , a>0, then u=a or u=-a

In this case a=12, which is greater 0. Then, the first condition becomes

Solving for x

The second condition becomes

Solving for x

Then, the value of x is -4 or 8.

Explanation:

In this question, we need to find the ratio of dimes to quarters.

If we let x be number of pennies in the bottle. Then,

Number of quarters in the bottle = 4x

Number of nickels in the bottle = 3x

Number of dimes in the bottle =5(3x)=15x

Now relating dimes to quarters, we have

Thus, there are 15 times as many dimes as pennies in the box.