MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
A student tried to solve the inequality −2(3x−5)+7≤x+4(1−2x). The work shown is reproduced below:
Step 1 −6x+10+7≤x+4−8x
Step 2 −6x+17≤−7x+4
Step 3 Add 7x to both sides: x+17≤4
Step 4 Subtract 17 from both sides: x≤−13
Answer the questions given below.
(i) Examine each step and identify the first step in which an error occurs. State the reason for the error.
(ii) Rewrite the complete, correct solution of the inequality, showing all intermediate steps.
(iii) Represent the final solution set on a number line and write it in interval notation.