Chapter 7

(a) If \(3 x^{2}+13 x+4=(x+4) \times\) a polynomial, state the degree of the polynomial. (b) What is the coefficient of \(x\) in this unknown polynomial?

Explain what is meant by the phrase ' \(a\) is inversely proportional to \(b\) '.

Solve the equation \(15-3 x=3(x-7)+11\).

Verify that the given value is a solution of the given equation. $$ 8 x-3=-11, x=-1 $$

Given \(a\) is proportional to \(b\), state which of the following are true and which are false: (a) when \(a\) doubles, then \(b\) also doubles (b) when \(a\) is halved, then \(b\) is doubled (c) a graph of \(a\) against \(b\) is a straight line graph (d) \(a\) divided by \(b\) is a constant

Rewrite each of the statements without using a modulus sign: $$ |x|<5 $$

Solve the equation \(\frac{x+2}{5}+3=\frac{x}{7}\).

If \(2 x^{2}+5 x+2=(x+2) \times\) a polynomial what must be the coefficient of \(x\) in this unknown polynomial?

Verify that the given value is a solution of the given equation. $$ 2 x+3=4, x=\frac{1}{2} $$

Solve the simultaneous equations $$ 3 x-2 y=11,5 x+7 y=39 $$