GCSE maths exercises for Year X based on algebraic expressions.

How to simplify a simple algebraic expression-

In some languages other than English, one distinguishes between ‘variables’ in functions and ‘unknown quantities’ in equations (‘incógnita’ in Portuguese/Spanish, ‘inconnue’ in French) but this does not completely clarify the situation. The terms such as variable and parameter cannot be precisely defined at this stage and are best left to be introduced later in the development of algebra.

An algebraic expression is an expression involving numbers, parentheses, operation signs and pronumerals that becomes a number when numbers are substituted for the pronumerals. For example 2x + 5 is an expression but +) × is not.

Examples of algebraic expressions are:

3x + 1 and 5(x2 + 3x)

As discussed later in this module the multiplication sign is omitted between letters and between a number and a letter. Thus substituting x = 2 gives

3x + 1 = 3 × 2 + 1 = 7  and  5(x2 + 3x) = 5(22 + 3 × 2) = 30.

 the emphasis is on expressions, and on the connection to the arithmetic that students have already met with whole numbers and fractions. The values of the pronumerals will therefore be restricted to the whole numbers and non-negative fractions.

Simplifying the following expression:

Example-1

(2x + 3) - (x - 4)

To simplify this expression, we can use the distributive property of multiplication over addition/subtraction. Here's how:

(2x + 3) - (x - 4) = 2x + 3 - x + 4 (distribute the negative sign) = x + 7 (combine like terms)

So the simplified expression is x + 7.

Example-2 -

Solve for x in the following equation:

2x + 5 = 13

To solve for x, we need to isolate x on one side of the equation. We can start by subtracting 5 from both sides:

2x + 5 - 5 = 13 - 5

Simplifying the left side:

2x = 8

Next, we can isolate x by dividing both sides by 2:

2x/2 = 8/2

Simplifying the left side:

x = 4

Exampl-3-

If x -1 0 = 100

then x = 100 + 10

so x = 110

Your turn-

• Find the value of 2x + 3 if x = 4.’ In this case the pronumeral is given the value 4

• Solve the equation for x: 2x + 5 = 3x - 2

• Find the value of X from the equation  5x + 12 = 2x + 3 

• Factorize the expression: 6x - 11x - 10 = 5

• Solve the inequality: 4x + 7 > 3x + 9

I hope these exercises are helpful! Let me know if you need any further assistance.

well done!