# Video: AQA GCSE Mathematics Foundation Tier Pack 3 β’ Paper 3 β’ Question 28

Solve 13π₯ β 20 = 5(π₯ β 3) to find π₯.

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### Video Transcript

Solve 13π₯ minus 20 is equal to five multiplied by π₯ minus three to find π₯.

In order to solve any linear equation, we need to work out the value of π₯ 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 π₯ is equal to a number.

Letβ²s firstly consider the right-hand side of the equation, five multiplied by π₯ minus three. We need to expand or multiply out this bracket by multiplying the five by π₯ and the five by negative three. Five multiplied by π₯ is equal to five π₯, 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 13π₯ minus 20 is equal to five π₯ 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 13π₯. On the right-hand side, negative 15 plus 20 is equal to positive five. Weβre left with five π₯ plus five.

Our next step is to get all the π₯s on one side of the equation. We do this by subtracting five π₯ from both sides. 13π₯ minus five π₯ is equal to eight π₯, as 13 minus five equals eight. Subtracting five π₯ from the right-hand side means that the five π₯s cancel. This leaves us with eight π₯ is equal to five. Eight π₯ means eight multiplied by π₯. 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 π₯ divided by eight is equal to π₯, and five divided by eight is equal to five-eighths or five over eight. This means that the solution to the equation 13π₯ minus 20 equals five multiplied by π₯ minus three is π₯ is equal to five-eighths.

We can check this answer by substituting our value for π₯ into the left-hand side and the right-hand side of the equation. If these two answers are equal, then our answer of π₯ equals five-eighths will be correct. Substituting π₯ 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 π₯ 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 π₯ equals five-eighths is correct.