Question

masteryconnect
scott, trinity
cgw 25-26 alg 1 semester exam
6 of 50
choose all examples of an equation with infinitely many solutions.
□ 5(2x + 4) = 10(x + 2)
□ 4(2x + 1) = 8x + 6
□ 2x - 5 - 13 = 2(x - 9)
□ 6x - 5 = 5x - 7
□ 4x + 7 = 4x - 5

Explanation:

Step1: Analyze each equation

For an equation \( ax + b = cx + d \) (after simplifying both sides), if \( a = c \) and \( b = d \), it has infinitely many solutions. Let's simplify each option:

Option 1: \( 5(2x + 4) = 10(x + 2) \)

Expand left side: \( 10x + 20 \)
Expand right side: \( 10x + 20 \)
Since both sides are equal (\( 10x + 20 = 10x + 20 \)), this equation has infinitely many solutions.

Option 2: \( 4(2x + 1) = 8x + 6 \)

Expand left side: \( 8x + 4 \)
Right side: \( 8x + 6 \)
\( 8x + 4
eq 8x + 6 \) (since \( 4
eq 6 \)), so no solution.

Option 3: \( 2x - 5 - 13 = 2(x - 9) \)

Simplify left side: \( 2x - 18 \)
Expand right side: \( 2x - 18 \)
Both sides are equal (\( 2x - 18 = 2x - 18 \)), so infinitely many solutions.

Option 4: \( 6x - 5 = 5x - 7 \)

Subtract \( 5x \) from both sides: \( x - 5 = -7 \)
Add 5 to both sides: \( x = -2 \) (one solution)

Option 5: \( 4x + 7 = 4x - 5 \)

Subtract \( 4x \) from both sides: \( 7 = -5 \) (false, no solution)

Step2: Identify equations with infinite solutions

From the analysis, the equations \( 5(2x + 4) = 10(x + 2) \) and \( 2x - 5 - 13 = 2(x - 9) \) have infinitely many solutions.

Answer:

The equations with infinitely many solutions are:

• \( 5(2x + 4) = 10(x + 2) \)
• \( 2x - 5 - 13 = 2(x - 9) \)