CAIE A-Level Mathematics AS 2.1.1 Modulus Equations Questions

Draw V-shaped graph with vertex on positive x-axis
Draw (more or less) correct graph of y=2 x+7 with smaller gradient
And crossing y-axis above y-intercept of modulus graph.

Solve 3 x-5=2 x+7 to obtain x=12
Attempt solution of linear equation where signs of 3 x and 2 x are
different
3 x-5=-2 x-7 OE.

Obtain $x=-\frac{2}{5}$
Alternative solution for question 4(b)

State or imply non-modulus equation $(3 x-5)^{2}=(2 x+7)^{2}$
Must be working with $(3 x-5)^{2}=(2 x+7)^{2}$.

Attempt solution of 3-term quadratic equation
Obtain $-\frac{2}{5}$ and 12

Apply logarithms and use power law for $3^{y}=k$ where k>0 or
correct equivalent
Using their positive answer from part (b)
or greater accuracy;
and no other values.

Obtain 2.26