Solved on Jan 19, 2024

Solve the linear equation $-8(-x+7)=8(x-7)$ and determine the number of solutions.

STEP 1

Assumptions
1. We are given the equation $-8(-x+7)=8(x-7)$ .
2. We need to determine if the equation has no solution, infinitely many solutions, or one solution.

STEP 2

First, we will distribute the $-8$ and $8$ on both sides of the equation to remove the parentheses.
$-8(-x+7)=8(x-7)$

STEP 3

Distribute $-8$ to both terms inside the parentheses on the left side.
$-8(-x) + (-8)(7) = 8(x-7)$

STEP 4

Distribute $8$ to both terms inside the parentheses on the right side.
$-8(-x) + (-8)(7) = 8(x) - 8(7)$

STEP 5

Simplify the multiplication.
$8x - 56 = 8x - 56$

STEP 6

We observe that both sides of the equation are identical, which implies that for any value of $x$ , the equation will hold true.

STEP 7

Since the equation is true for any value of $x$ , the equation has infinitely many solutions.
The equation $-8(-x+7)=8(x-7)$ has infinitely many solutions.

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Solve the linear equation $-8(-x+7)=8(x-7)$ and determine the number of solutions.

STEP 1

Assumptions
1. We are given the equation $-8(-x+7)=8(x-7)$ .
2. We need to determine if the equation has no solution, infinitely many solutions, or one solution.

STEP 2

First, we will distribute the $-8$ and $8$ on both sides of the equation to remove the parentheses.
$-8(-x+7)=8(x-7)$

STEP 3

Distribute $-8$ to both terms inside the parentheses on the left side.
$-8(-x) + (-8)(7) = 8(x-7)$

STEP 4

Distribute $8$ to both terms inside the parentheses on the right side.
$-8(-x) + (-8)(7) = 8(x) - 8(7)$

STEP 5

Simplify the multiplication.
$8x - 56 = 8x - 56$

STEP 6

We observe that both sides of the equation are identical, which implies that for any value of $x$ , the equation will hold true.

STEP 7

Since the equation is true for any value of $x$ , the equation has infinitely many solutions.
The equation $-8(-x+7)=8(x-7)$ has infinitely many solutions.

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Solve the linear equation −8(−x+7)=8(x−7)-8(-x+7)=8(x-7)−8(−x+7)=8(x−7) and determine the number of solutions.

STEP 1

Assumptions1. We are given the equation −8(−x+7)=8(x−7)-8(-x+7)=8(x-7)−8(−x+7)=8(x−7).2. We need to determine if the equation has no solution, infinitely many solutions, or one solution.

STEP 2

First, we will distribute the −8-8−8 and 888 on both sides of the equation to remove the parentheses.−8(−x+7)=8(x−7)-8(-x+7)=8(x-7)−8(−x+7)=8(x−7)

STEP 3

Distribute −8-8−8 to both terms inside the parentheses on the left side.−8(−x)+(−8)(7)=8(x−7)-8(-x) + (-8)(7) = 8(x-7)−8(−x)+(−8)(7)=8(x−7)

STEP 4

Distribute 888 to both terms inside the parentheses on the right side.−8(−x)+(−8)(7)=8(x)−8(7)-8(-x) + (-8)(7) = 8(x) - 8(7)−8(−x)+(−8)(7)=8(x)−8(7)

STEP 5

Simplify the multiplication.8x−56=8x−568x - 56 = 8x - 568x−56=8x−56

STEP 6

We observe that both sides of the equation are identical, which implies that for any value of xxx, the equation will hold true.

STEP 7

Since the equation is true for any value of xxx, the equation has infinitely many solutions.The equation −8(−x+7)=8(x−7)-8(-x+7)=8(x-7)−8(−x+7)=8(x−7) has infinitely many solutions.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the linear equation $-8(-x+7)=8(x-7)$ and determine the number of solutions.

Assumptions
1. We are given the equation $-8(-x+7)=8(x-7)$ .
2. We need to determine if the equation has no solution, infinitely many solutions, or one solution.

First, we will distribute the $-8$ and $8$ on both sides of the equation to remove the parentheses.
$-8(-x+7)=8(x-7)$

Distribute $-8$ to both terms inside the parentheses on the left side.
$-8(-x) + (-8)(7) = 8(x-7)$

Distribute $8$ to both terms inside the parentheses on the right side.
$-8(-x) + (-8)(7) = 8(x) - 8(7)$

Simplify the multiplication.
$8x - 56 = 8x - 56$

We observe that both sides of the equation are identical, which implies that for any value of $x$ , the equation will hold true.

Since the equation is true for any value of $x$ , the equation has infinitely many solutions.
The equation $-8(-x+7)=8(x-7)$ has infinitely many solutions.