Exercise solution 2, page 252 - Mathematics Foundation Student Book

⭐ What you need to know:

A) In these questions, you are asked to find the value of x when y = 0. This means you must replace every y in the equation by \(0\), then solve the new equation.

For example, if \(y + 3x = 14\) and \(y=0\), then:

\[\begin{aligned} 0 + 3x &= 14 \\ 3x &= 14 \end{aligned}\]

B) After substituting \(y=0\), simplify the equation carefully. Adding \(0\) does not change a number, and multiplying by \(0\) gives \(0\).

Useful facts:

\[ a+0=a \qquad\text{and}\qquad 0\times a=0 \]

For example, if \(4y - 5x = 18\) and \(y=0\), then:

\[\begin{aligned} 4\times 0 - 5x &= 18 \\ 0 - 5x &= 18 \\ -5x &= 18 \end{aligned}\]

C) To solve for x, use inverse operations. The aim is to get x on its own.

If \(x\) is multiplied by a number, divide both sides by that number. For example:

\[\begin{aligned} 6x &= 24 \\ x &= \frac{24}{6} \\ x &= 4 \end{aligned}\]

If the coefficient of \(x\) is negative, the method is the same. For example:

\[\begin{aligned} -3x &= 15 \\ x &= \frac{15}{-3} \\ x &= -5 \end{aligned}\]

D) Keep the equation balanced: whatever you do to one side, you must do to the other side as well. This is the key idea when solving equations.

For example:

\[\begin{aligned} x + 9 &= 17 \\ x + 9 - 9 &= 17 - 9 \\ x &= 8 \end{aligned}\]

E) It is helpful to check your answer by substituting your value of x back into the equation, together with \(y=0\). If both sides are equal, your answer is correct.

For example, if you found \(x=7\) for the equation \(y + 2x = 14\), check it like this:

\[\begin{aligned} y + 2x &= 14 \\ 0 + 2\times 7 &= 14 \\ 14 &= 14 \end{aligned}\]

Since both sides are equal, the value is correct.