Solving an Equation by Multiplication/ Division: Exercises on Both Sides (of the Equation)

First, we arrange the two sections so that the right side contains the values with the coefficient x and the left side the numbers without the x

Let's remember to maintain the plus and minus signs accordingly when we move terms between the sections.

First, we move a$5x$ to the right section and then the 22 to the left side. We obtain the following equation:

$-8-22=10x-5x$

We subtract both sides accordingly and obtain the following equation:

$-30=5x$

We divide both sections by 5 and obtain:

$-6=x$

To solve the equation $6 - 7x = -5x + 8$, we will follow these steps:

• Step 1: Move all terms involving $x$ to one side of the equation by adding $5x$ to both sides.
• Step 2: Simplify both sides of the equation.
• Step 3: Solve for $x$.

Now, let's work through each step:

Step 1: Add $5x$ to both sides to move the $x$-term to the left side:

$6 - 7x + 5x = 8$

Step 2: Simplify the equation by combining the $x$-terms on the left side:

$6 - 2x = 8$

Step 3: To isolate $-2x$ on the left, subtract $6$ from both sides:

$-2x = 8 - 6$

Simplify the right side:

$-2x = 2$

Finally, divide both sides by $-2$ to solve for $x$:

$x = \frac{2}{-2}$

$x = -1$

Therefore, the solution to the problem is $x = -1$.

First, we solve the multiplication and division exercises, we will put them in parentheses to avoid confusion:

$92-(x\times2)-(24\colon4)=64$

$92-2x-6=64$

Reduce:

$86-2x=64$

Move the sides:

$-2x=64-86$

$-2x=-22$

Divide by negative 2:

$x=\frac{-22}{-2}$

$x=11$