Math / Algebra

QuestionSolve the equation for $x$ . $-2(5 x-3)+8=-10 x+14$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $x=$ $\square$ (Type an integer or a fraction. Simplify your answer.) B. The solution is all real numbers. C. There is no solution.

Studdy Solution

STEP 1

1. The equation $-2(5x - 3) + 8 = -10x + 14$ is a linear equation in one variable.
2. We need to simplify and solve for $x$ .
3. The solution could be a specific value, all real numbers, or no solution.

STEP 2

1. Simplify both sides of the equation.
2. Collect like terms and isolate the variable $x$ .
3. Determine the solution type based on the simplified equation.

STEP 3

Distribute the $-2$ on the left side of the equation:
$-2(5x - 3) = -2 \cdot 5x + (-2) \cdot (-3) = -10x + 6$
So the equation becomes:
$-10x + 6 + 8 = -10x + 14$

STEP 4

Combine the constant terms on the left side:
$-10x + 14 = -10x + 14$

STEP 5

Notice that both sides of the equation are identical:
$-10x + 14 = -10x + 14$
This implies that the equation is true for all values of $x$ .

STEP 6

Since the equation is true for all values of $x$ , the solution is:
B. The solution is all real numbers.

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QuestionSolve the equation for $x$ . $-2(5 x-3)+8=-10 x+14$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $x=$ $\square$ (Type an integer or a fraction. Simplify your answer.) B. The solution is all real numbers. C. There is no solution.

Studdy Solution

STEP 1

1. The equation $-2(5x - 3) + 8 = -10x + 14$ is a linear equation in one variable.
2. We need to simplify and solve for $x$ .
3. The solution could be a specific value, all real numbers, or no solution.

STEP 2

1. Simplify both sides of the equation.
2. Collect like terms and isolate the variable $x$ .
3. Determine the solution type based on the simplified equation.

STEP 3

Distribute the $-2$ on the left side of the equation:
$-2(5x - 3) = -2 \cdot 5x + (-2) \cdot (-3) = -10x + 6$
So the equation becomes:
$-10x + 6 + 8 = -10x + 14$

STEP 4

Combine the constant terms on the left side:
$-10x + 14 = -10x + 14$

STEP 5

Notice that both sides of the equation are identical:
$-10x + 14 = -10x + 14$
This implies that the equation is true for all values of $x$ .

STEP 6

Since the equation is true for all values of $x$ , the solution is:
B. The solution is all real numbers.

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Studdy Solution

STEP 1

1. The equation −2(5x−3)+8=−10x+14 -2(5x - 3) + 8 = -10x + 14 −2(5x−3)+8=−10x+14 is a linear equation in one variable.2. We need to simplify and solve for x x x.3. The solution could be a specific value, all real numbers, or no solution.

STEP 2

1. Simplify both sides of the equation.2. Collect like terms and isolate the variable x x x.3. Determine the solution type based on the simplified equation.

STEP 3

Distribute the −2-2−2 on the left side of the equation:−2(5x−3)=−2⋅5x+(−2)⋅(−3)=−10x+6 -2(5x - 3) = -2 \cdot 5x + (-2) \cdot (-3) = -10x + 6 −2(5x−3)=−2⋅5x+(−2)⋅(−3)=−10x+6So the equation becomes:−10x+6+8=−10x+14 -10x + 6 + 8 = -10x + 14 −10x+6+8=−10x+14

STEP 4

Combine the constant terms on the left side:−10x+14=−10x+14 -10x + 14 = -10x + 14 −10x+14=−10x+14

STEP 5

Notice that both sides of the equation are identical:−10x+14=−10x+14 -10x + 14 = -10x + 14 −10x+14=−10x+14This implies that the equation is true for all values of x x x.

STEP 6

Since the equation is true for all values of x x x, the solution is:B. The solution is all real numbers.

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Studdy solves anything!

Start learning now

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

1. The equation $-2(5x - 3) + 8 = -10x + 14$ is a linear equation in one variable.
2. We need to simplify and solve for $x$ .
3. The solution could be a specific value, all real numbers, or no solution.

1. Simplify both sides of the equation.
2. Collect like terms and isolate the variable $x$ .
3. Determine the solution type based on the simplified equation.

Distribute the $-2$ on the left side of the equation:
$-2(5x - 3) = -2 \cdot 5x + (-2) \cdot (-3) = -10x + 6$
So the equation becomes:
$-10x + 6 + 8 = -10x + 14$

Combine the constant terms on the left side:
$-10x + 14 = -10x + 14$

Notice that both sides of the equation are identical:
$-10x + 14 = -10x + 14$
This implies that the equation is true for all values of $x$ .

Since the equation is true for all values of $x$ , the solution is:
B. The solution is all real numbers.