Question

i) 2r - 12 = \frac{r}{2} + 51

Explanation:

Step1: Eliminate fraction by multiplying all terms by 2.

Multiply each term in the equation \(2r - 12=\frac{r}{2}+ 51\) by 2 to get rid of the fraction. So we have \(2\times(2r)-2\times12 = 2\times\frac{r}{2}+2\times51\), which simplifies to \(4r - 24=r + 102\).

Step2: Subtract r from both sides.

Subtract \(r\) from both sides of the equation \(4r - 24=r + 102\) to get \(4r - r-24=r - r + 102\), which simplifies to \(3r-24 = 102\).

Step3: Add 24 to both sides.

Add 24 to both sides of the equation \(3r-24 = 102\). So we have \(3r-24 + 24=102 + 24\), which simplifies to \(3r=126\).

Step4: Divide both sides by 3.

Divide both sides of the equation \(3r = 126\) by 3. So \(\frac{3r}{3}=\frac{126}{3}\), which gives \(r = 42\).

Answer:

\(r = 42\)