Question

1. find the perimeter of the square.
2. solve for b.

6b + 8 = 2(3b + 4)
does the equation have (circle one)
a. one solution
b=
b. no solution
c. ims
infinitely many solutions

1. solve for p.

5p - 3p = 2(p + 4)
does the equation have (circle one)
a. one solution
p=
b. no solution
c. ims
infinitely many solutions

1. solve for w.

6w - 2 = 8w + 16
does the equation have (circle one)
d. one solution
w=
e. no solution
f. ims
infinitely many solutions
honors only
solve for x
5(8y + 4) - 72y = 2y - 3(4y + 8)

Explanation:

Problem 6: Find the perimeter of the square

Step 1: Recall square properties

A square has 4 equal sides. From the diagram, one side is \( x + 16 \) and another is \( 5x \). Since it's a square, these sides are equal: \( x + 16 = 5x \).

Step 2: Solve for \( x \)

Subtract \( x \) from both sides: \( 16 = 4x \). Divide by 4: \( x = 4 \).

Step 3: Find side length

Substitute \( x = 4 \) into \( 5x \): \( 5(4) = 20 \). So each side is 20.

Step 4: Calculate perimeter

Perimeter of square is \( 4 \times \text{side} \), so \( 4 \times 20 = 80 \).

Step 1: Expand right side

\( 2(3b + 4) = 6b + 8 \).

Step 2: Simplify equation

Left side: \( 6b + 8 \), right side: \( 6b + 8 \). So \( 6b + 8 = 6b + 8 \), which is true for all \( b \).

Step 1: Simplify left side

\( 5p - 3p = 2p \).

Step 2: Expand right side

\( 2(p + 4) = 2p + 8 \).

Step 3: Simplify equation

\( 2p = 2p + 8 \). Subtract \( 2p \): \( 0 = 8 \), which is false.

Answer:

80

Problem 7: Solve for \( b \) in \( 6b + 8 = 2(3b + 4) \)