Solving equations with brackets
Remember to remove brackets, multiply the term on the outside of the bracket with each term inside the bracket.
Example
Solve the equation \(4(5 - 2x) - 5 = 39\)
Answer
\(4(5 - 2x) - 5 = 39\)
Remember BODMAS tells us to remove the brackets first
\(20 - 8x - 5 = 39\)
Remember change side, change operation
\(- 8x = 39 - 20 + 5\)
\(- 8x = 24\)
\(x = \frac{{24}}{{ - 8}} = \frac{3}{{ - 1}} = - 3\)
Now try the example questions below.
Question
Solve the equation \(4x - 2(1 - 3x) = 3\)
\(4x - 2(1 - 3x) = 3\)
\(4x - 2 + 6x = 3\)
Remember when you subtract a negative, you add.
\(4x + 6x = 3 + 2\)
Remember letters to the left, numbers to the right.
\(10x = 5\)
\(x = \frac{1}{2}\)
Question
Solve the equation \(3(7 - 2x) = 3(x + 5) - 84\)
\(3(7 - 2x) = 3(x + 5) - 84\)
Remove the brackets first.
\(21 - 6x = 3x + 15 - 84\)
Letters to the left, numbers to the right.
\(- 6x - 3x = 15 - 84 - 21\)
\(- 9x = - 90\)
\(x = \frac{{ - 90}}{{ - 9}} = \frac{{10}}{1} = 10\)
Question
For the The simplest two-dimensional shape is the triangle, a three-sided shape with three angles. below, write down an equation involving \(x^\circ\) then solve to find the sizes of the angles at each The point where two lines meet is called the vertex. In a 3D shape this is the corner point..
Remember the angles in a triangle add up to 180°, so the equation for the above triangle is:
\((2x^\circ + 34^\circ ) + 6x^\circ + 50^\circ = 180^\circ\)
\(8x^\circ + 84^\circ = 180^\circ\)
\(8x^\circ = 180^\circ - 84^\circ\)
\(8x^\circ = 96^\circ\)
\(x^\circ = \frac{{96^\circ }}{{8^\circ }} = 12^\circ\)
Therefore the angles in the triangle above are 50°, 72° and 58°.
More guides on this topic
- Expansion of brackets
- Factorising an algebraic expression
- Completing the square in a quadratic expression
- Simplifying algebraic fractions
- Applying the four operations to algebraic fractions
- Determining the equation of a straight line
- Working with simultaneous equations
- Changing the subject of a formula
- Determine the equation of a quadratic function from its graph
- Sketching a quadratic function
- Identifying features of a quadratic function
- Solving a quadratic equation
- Solving a quadratic equation using the quadratic formula
- Using the discriminant to determine the number of roots
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