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

Solve 13π‘₯ βˆ’ 20 = 5(π‘₯ βˆ’ 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. We’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.

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