G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

 

Year 10 Interactive Maths - Second Edition


Equations Involving Two or More Operations

To solve a linear equation, we apply the same operations to both sides of the equation to collect numerical terms on the right-hand side and pronumeral terms on the left-hand side.

Example 5

Solve 2p + 7 = 20 for p.

Solution:

Subtract 7 from both sides and then divide both sides by 2 to find p = 6 1/2.

Setting Out:

We can set out the solution as follows:

The solution can be set out in three lines.

Check:

LHS = 2p + 7 = 2 times 6.5 + 7 = 20 = RHS, so our solution, p = 6 1/2, is correct.


Example 6

Solve 8x + 3 = 5x + 18 for x.

Solution:

Subtract 3 from both sides, then subtract 5x from both sides and finally divide both sides by 3 to find x = 5.

Setting Out:

We can set out the solution as follows:

The solution can be set out in four lines.

Check:

Substitute x = 5 into the LHS to find LHS = 43.

Substitute x = 5 into the RHS to find RHS = 43.

Therefore, LHS = RHS.  So, our solution, x = 5, is correct.

 

Study Another Topic in Chapter 2: Linear Equations and Inequalities

Solving Equations ] [ Equations Involving Two or More Operations ] Equations Containing Brackets ] Equations Containing Fractions ] Problem Solving ] Consecutive Numbers ] Solving Inequalities ] Adding a Number to Each Side of an Inequality ] Multiplying Each Side of an Inequality by a Positive Number ] Dividing Each Side of an Inequality by a Positive Number ] Multiplying Each Side of an Inequality by a Negative Number ] Dividing Each Side of an Inequality by a Negative Number ] Inequalities Involving Two Operations ] Inequalities Containing Brackets ] Inequalities Containing Fractions ] Transposition of Formulas ] Transpositions Involving Subtraction ] Transpositions Involving Division ] Transpositions Involving Multiplication ] Transpositions Involving Squares ] Transpositions Involving Square Roots ] Transpositions Involving Brackets ] Transpositions Involving Fractions ] Transpositions Involving Two or More Operations ] Subject Occurring Twice ] Substitution ] Problem Solving ] Problem Solving Unit ] Symbols ] Index ]

 

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