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<p>Solve the following equations.</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">$\frac{4(-2x+3)}{9}-3=-\frac{(-7)(x+6)}{12}-\frac{13}{6}$<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">$\frac{\frac{4}{3}\left(9x+\frac{2}{5}\right)}{8}=-\frac{\left(-\frac{3}{4}\right)\left(\frac{1}{2}x-3\right)}{\frac{3}{2}}$<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">$\frac{1}{5-2x}+\frac{3}{2x+5}=\frac{1}{4x^2-25}$<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-iv" data-list-item-path="item-iv"><div class="list-item-paragraph">$\frac{1}{(3x-8)}+\frac{2}{(3x-8)^2}=\frac{1}{9x^2-48x+64}$<span class="inline-marks">[2]</span></div></li></ol>

Solving Equations involving Algebraic Fractions

Solving Linear Equations

IP1 Class Test (May 2025) Q11

Algebraic Expressions, Identities and Formulae

Linear Equations and Inequalities

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{a - 2}{3} - \frac{1 - a}{2} = \frac{1}{5}(5a - 4)$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{3b + 3}{b - 1} = -\frac{7}{2}$</span></div></li></ol>

$\frac{a - 2}{3} - \frac{1 - a}{2} = \frac{1}{5}(5a - 4)$

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{6x - 2}{3} - \frac{x}{2} = -\frac{1}{3}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{2 - 3y}{1 - y} = \frac{2}{5}$</span></div></li></ol>

$\frac{6x - 2}{3} - \frac{x}{2} = -\frac{1}{3}$

<p>Given $x - y = 7x + 3y$, find the value of $\frac{5x}{4y}$.</p>

Given $x - y = 7x + 3y$, find the value of $\frac{5x}{4y}$.

<p>Given $3a - 5b = 6a - 2b$, find the value of $\frac{a}{2b}$.</p>

Given $3a - 5b = 6a - 2b$, find the value of $\frac{a}{2b}$.

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{3x - 1}{2} = \frac{5 - 2x}{3}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{5y - 3}{4} - \frac{4 - 5y}{3} = 0$</span></div></li></ol>

$\frac{5y - 3}{4} - \frac{4 - 5y}{3} = 0$

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{3(2a - 1)}{10} + \frac{5(4 - a)}{4} = 0$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{4b + 3}{2} - \frac{b + 1}{7} = 0$</span></div></li></ol>

$\frac{3(2a - 1)}{10} + \frac{5(4 - a)}{4} = 0$

 Solving Linear Equations

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{2}{3} (3x - 1) = \frac{1}{4} (1 - x)$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{4(2x - 1)}{5} = \frac{x + 1}{2}$</span></div></li></ol>

$\frac{2}{3} (3x - 1) = \frac{1}{4} (1 - x)$

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{y}{4} = \frac{5}{2}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{2t}{3} = \frac{3}{4}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{1}{x - 1} = \frac{1}{5}$</span></div></li></ol>

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{9}{a} = \frac{3}{11}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{3b}{14} = \frac{2}{7}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{3}{2c - 5} = \frac{1}{3}$</span></div></li></ol>

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\frac{2}{x} = \frac{6}{7}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{y}{4} = \frac{5}{3}$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\frac{12}{z - 3} = \frac{2}{5}$</span></div></li></ol>

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$2.5 \ (1.9x + 3.6) = 8.6$</div></li><li><div class="list-item-paragraph">$0.4 \ (6.8y - 1) = 5.5$</div></li></ol>

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$0.3\ (1 - 3x) = -2\ (x - 3)$</div></li><li><div class="list-item-paragraph">$\frac{5}{4}\ (3 - y) = 2\ (4y - 1)$</div></li></ol>

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$2\ (4 - y) = -5\ (3y + 4)$</div></li><li><div class="list-item-paragraph">$5 - 2\ (1 - x) = -3\ (x + 1)$</div></li></ol>

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$5a + 3 = 18$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$2b - 3 = 5b + 4$</span></div></li><li><div class="list-item-paragraph">$2k - 3 = 5\ (4 - k)$</div></li></ol>

<p>Solve each of the following equations.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$ 3x - 1 = 5 $</div></li><li><div class="list-item-paragraph">$ 4 - 7x = 18 $</div></li><li><div class="list-item-paragraph">$ 5 - 2\ (1 - x) = 11 $</div></li></ol>

<p>Solve the following equation $\frac{5(3x-2)}{6}-3x=-2\frac{2}{3}$.</p>

Solve the following equation $\frac{5(3x-2)}{6}-3x=-2\frac{2}{3}$.

[EPQ Vol 1A] Question 23

<p>Solve $3\left( 3x-\frac{1}{3} \right)=6-4(2-x)$.</p>

Solve $3\left( 3x-\frac{1}{3} \right)=6-4(2-x)$.

[EPQ Vol 1A] Question 22

<p>Solve each of the following equations.

</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$14=0.84\left( 2-3a \right)$
</div></li><li><div class="list-item-paragraph">$7.4=-3\left( 6-b \right)$</div></li></ol>

[EPQ Vol 1A] Question 17

<p>Solve the following equations.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$3-\frac{x}{6}=\frac{5x+12}{10}$</div></li><li><div class="list-item-paragraph">$\frac{7r-4}{5}-\frac{3(r+1)}{4}=\frac{2(2r-4)}{3}$</div></li></ol>

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