Question

I need to learn linear equations.-9 - 4x = -53

Answer 1

For the linear equation given;

`-9-4x=-53`

It is important to note that whatever we do on the right side, we must do the same on the left side.

The Left side is;

`-9-4x`

While the Right side is;

`-53`

To calculate the unknown variable, which in this case is x, we would first of all isolate any term(s) that inculdes x, as shown below;

`\begin{gathered} -9-4x=-53 \\ To\text{ isolate -4x, we need to remove -9 from the left side} \\ We\text{ do this by including +9 on the left side} \\ \text{That means, }add\text{ 9 the left side} \end{gathered}`

Remember however that one rule we must never forget is that whatever you do on the left you must do the same on the right, and vice versa. Therefore, our first step would be,

"Add 9 to both sides of the equation."

`\begin{gathered} -9-4x=-53 \\ \text{Add 9 to both sides of the equation} \\ -9+9-4x=-53+9 \end{gathered}`

Where we have -9 + 9 (or +9 - 9) that equals zero. Hence;

`\begin{gathered} 0-4x=-53+9_{} \\ OR \\ 0-4x=9-53 \\ -4x=-44 \end{gathered}`

Next we try to isolate x by removing -4, as follows;

`\begin{gathered} -4x=-44 \\ \text{Divide both sides by -4} \end{gathered}`

We are dividing here because -4x is actually -4 times x. The opposite of multiplication is division, the same way the opposite of addition is subtraction.

We can now complete the solution as shown below;

`\begin{gathered} -4x=-44 \\ \text{Divide both sides by -4} \\ (-4x)/(-4)=(-44)/(-4) \\ x=11 \end{gathered}`

ANSWER:

x = 11