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In part a)

$\\simplify{x+{b[0]}={c[0]}}$

On isolating $x$ to one side,

$x= \\var{c[0]}-\\var{b[0]}$

$x= \\var{d}$

In part b)

$\\simplify{{a[1]}x={c[1]}}$

Solve for $x$,

$x= \\frac{\\var{c[1]}}{\\var{a[1]}}$

$x= \\var{f}$

In part c)

$\\simplify{{a[2]}/{af}x={c[2]}}$

$x= \\frac{\\var{c[2]}*\\var{af}}{\\var{a[2]}}$

$x= \\var{g}$

The video below explains how to carry out similar problems.

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$\\simplify{x+{b[0]}={c[0]}}$

$x=$ [[0]]

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$\\simplify{{a[1]}x={c[1]}}$

$x=$ [[0]]

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$\\simplify{{a[2]}/{af}x={c[2]}}$

$x=$ [[0]]

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When the coefficient of $x$ is a fraction, you follow the same steps but have to consider how we divide by a fraction.

For example,

We start with: $\\frac{3}{4}x=6$

We 'divide both sides' by the coefficient of $x$: $\\frac{\\frac{3}{4}x}{\\frac{3}{4}}=\\frac{6}{\\frac{3}{4}}$

The coefficient of $x$ cancels: $x=\\frac{6}{\\frac{3}{4}}$

Now, to divide $6$ by $\\frac{3}{4}$, you can also multipliy $6$ by the fraction reciprocal (flipped): $x=6\\times\\frac{4}{3}$

When simplified, we're left with the final answer: $x=8$

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Evaluate $x$ in the following equations (give your answer correct to two decimal places when the answer isn't an integer).

If you are not familiar with solving these kinds of equations, study this video for the basic theory.

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coefficient of x on lhs

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constant on rhs

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coefficient denominator

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Basic solving of linear equations.

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