Solve these inequalities. (a) \(x+7\ge 12\) [1] (b) \(4x\lt 26\) [2]
Question 1 Report
Solve these inequalities.
(a) \(x+7\ge 12\) [1]
(b) \(4x\lt 26\) [2]
Answer Details
An inequality is solved just like an equation: do the same thing to both sides until the letter stands alone. The one extra rule is that multiplying or dividing by a negative number reverses the symbol, which is not needed here since both operations involve positive numbers.
(a) Subtract \(7\) from both sides:
\[ x+7-7\ge 12-7\quad\Rightarrow\quad x\ge 5 \] [B1]
The symbol \(\ge\) is unchanged, so \(x=5\) is itself a solution.
(b) Divide both sides by \(4\):
\[ x\lt\frac{26}{4} \] [M1]
\[ x\lt 6.5 \] [A1]
Leaving the answer as \(\frac{26}{4}\) or \(\frac{13}{2}\) is acceptable, but \(6.5\) is the tidiest form.
A frequent error is to change \(\lt\) into \(=\) partway through and give a single value such as \(x=6.5\). The solution of an inequality is a whole range of numbers, so the symbol must be carried through to the final line.
Download The App On Google Playstore
Everything you need to excel in your exams
