# Video: AQA GCSE Mathematics Foundation Tier Pack 3 • Paper 3 • Question 28

Solve 13𝑥 − 20 = 5(𝑥 − 3) to find 𝑥.

03:56

### Video Transcript

Solve 13𝑥 minus 20 is equal to five multiplied by 𝑥 minus three to find 𝑥.

In order to solve any linear equation, we need to work out the value of 𝑥 so that the left-hand side is equal to the right-hand side. One of the easiest ways to do this is to simplify the equation using the balancing method until we end up with 𝑥 is equal to a number.

Let′s firstly consider the right-hand side of the equation, five multiplied by 𝑥 minus three. We need to expand or multiply out this bracket by multiplying the five by 𝑥 and the five by negative three. Five multiplied by 𝑥 is equal to five 𝑥, and five multiplied by negative three is equal to negative 15. Multiplying a positive number by a negative number gives us a negative answer. The equation is simplified to 13𝑥 minus 20 is equal to five 𝑥 minus 15.

Next, we can add 20 to both sides of the equation. On the left-hand side, negative 20 plus 20 is equal to zero. So we are just left with 13𝑥. On the right-hand side, negative 15 plus 20 is equal to positive five. We’re left with five 𝑥 plus five.

Our next step is to get all the 𝑥s on one side of the equation. We do this by subtracting five 𝑥 from both sides. 13𝑥 minus five 𝑥 is equal to eight 𝑥, as 13 minus five equals eight. Subtracting five 𝑥 from the right-hand side means that the five 𝑥s cancel. This leaves us with eight 𝑥 is equal to five. Eight 𝑥 means eight multiplied by 𝑥. The opposite or inverse of multiplying by eight is dividing by eight. Therefore, we need to divide both sides of the equation by eight. Eight 𝑥 divided by eight is equal to 𝑥, and five divided by eight is equal to five-eighths or five over eight. This means that the solution to the equation 13𝑥 minus 20 equals five multiplied by 𝑥 minus three is 𝑥 is equal to five-eighths.

We can check this answer by substituting our value for 𝑥 into the left-hand side and the right-hand side of the equation. If these two answers are equal, then our answer of 𝑥 equals five-eighths will be correct. Substituting 𝑥 equals five-eighths into the left-hand side of the equation gives us 13 multiplied by five-eighths minus 20. Typing this into our calculator gives us an answer of negative ninety-five eights. This is the same as negative 11 and seven-eighths or negative 11.875.

Substituting 𝑥 equals five-eighths into the right-hand side of the equation gives us five multiplied by five-eighths minus three. Once again, typing this into the calculator gives us an answer of negative ninety-five eighths. As the left-hand side of the equation and right-hand side give us the same answer, then our value for 𝑥 equals five-eighths is correct.