Question3. (i) $7(x-2)=2(2 x-4)$

Studdy Solution

STEP 1

1. The equation $7(x-2) = 2(2x-4)$ is a linear equation in one variable.
2. The goal is to solve for $x$ .
3. The equation involves distributing, combining like terms, and isolating the variable.

STEP 2

1. Expand both sides of the equation.
2. Simplify the equation by combining like terms.
3. Isolate the variable $x$ .
4. Verify the solution by substituting it back into the original equation.

STEP 3

Expand both sides of the equation by distributing the numbers outside the parentheses:
Left side: $7(x-2) = 7x - 14$
Right side: $2(2x-4) = 4x - 8$
The equation becomes:
$7x - 14 = 4x - 8$

STEP 4

To simplify the equation, move all terms involving $x$ to one side and constant terms to the other side. Subtract $4x$ from both sides:
$7x - 4x - 14 = -8$
This simplifies to:
$3x - 14 = -8$

STEP 5

Isolate the variable $x$ by adding 14 to both sides:
$3x - 14 + 14 = -8 + 14$
This simplifies to:
$3x = 6$
Now, divide both sides by 3 to solve for $x$ :
$x = \frac{6}{3}$
$x = 2$

STEP 6

Verify the solution by substituting $x = 2$ back into the original equation:
Original equation: $7(x-2) = 2(2x-4)$
Substitute $x = 2$ :
Left side: $7(2-2) = 7 \times 0 = 0$
Right side: $2(2 \times 2 - 4) = 2(4 - 4) = 2 \times 0 = 0$
Both sides are equal, confirming that the solution is correct.
The solution is:
$\boxed{2}$

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