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2. Scales Solving Equations 2x + 5 = 21 2x + 5 21 x x
An equation means that two things are equal. A pair of scales is sometimes used to show equations because when both sides balance they are equal.
The scales below show that the expression 2x + 5 is equal to the quantity 21, where x is the number of marbles in each bag.
2x + 5 = 21 x x
2x + 5 21
Scales

3. Solving Equations 2x + 5 = x + 10 2x + 5 x + 10 x x x
An equation means that two things are equal. A pair of scales is sometimes used to show equations because when both sides balance they are equal.
This pair of scales show that the expression 2x + 5 is equal to the expression x + 10, where x is the number of marbles in each bag.
2x + 5 = x + 10 x x x
2x + 5
x + 10

4. So solving 2x + 5 = 21 is equivalent to solving 2x = 16
Solving Equations
An equation means that two things are equal. A pair of scales is sometimes used to show equations because when both sides balance they are equal.
We could find the value of x (the solution to the equation) by removing equal numbers of marbles from each pan so that the scales remain balanced.
So solving 2x + 5 = 21 is equivalent to solving 2x = 16
2x + 5 = 21 x x
2x + 2 18
2x + 3 19 2x 16
2x + 5
2x + 1 17
2x + 4 20 21
x = 8
Check 2 x = 21

5. So solving 2x + 5 = 21 is equivalent to solving 2x = 16
Solving Equations
An equation means that two things are equal. A pair of scales is sometimes used to show equations because when both sides balance they are equal.
We could find the value of x (the solution to the equation) by removing equal numbers of marbles from each pan so that the scales remain balanced.
So solving 2x + 5 = 21 is equivalent to solving 2x = 16
We could of course have removed all 5 marbles at once.
2x + 5 = 21 x x
2x + 5 2x 16 21
x = 8
Check 2 x = 21

6. Solving Equations 2x + 6 = x + 9 2x + 6 x + 9 2x x + 3 x 3 So x = 3
An equation means that two things are equal. A pair of scales is sometimes used to show equations because when both sides balance they are equal.
In this equation we can remove 6 from each side to start with.
Followed by a bag from each side.
2x + 6 = x + 9 x x x
2x + 6
x + 9 2x
x + 3 x 3
So x = 3
Check 2 x = 12 = 6 + 3

7. Examples + - x  Solving Equations 2x + 6 = x + 9 2x + 6 = x + 9
When solving equations (without scales) we must follow the same principle as in the two previous examples.
x = 3
+ - x 
Whatever we do to one side of the equation we must do to the other.
2x + 6 = x + 9
Example Question 1: solve
2x + 6 = x + 9
Example Question 1: solve
Subtract 6 from both sides.
Subtract x from both sides.
2x = x + 3
Subtract x from both sides.
x + 6 = 9
Subtract 6 from both sides.
x = 3
x = 3
It makes no difference whether you do the x’s first and the numbers second.
Examples

8. + - x  Solving Equations 8x - 5 = 11 5p - 17 = - 2 8x = 16 5p = 15
2x + 6 = x + 9
Solving Equations
+ - x 
Whatever we do to one side of the equation we must do to the other.
x = 3
8x - 5 = 11
Example Question 2: solve
5p - 17 = - 2
Example Question 3: solve
Add 5 to both sides.
Add 17 to both sides.
8x = 16
Divide both sides by 8
5p = 15
Divide both sides by 5
x = 2
p = 3
3x - 5 = x + 11
Example Question 4: solve
7q + 6 = 3q + 10
Example Question 5: solve
Subtract x from both sides.
Subtract 3q from both sides.
2x - 5 = 11
Add 5 to both sides
4q + 6 = 10
Subtract 6 to both sides
4q = 4
2x = 16
Divide both sides by 2
Divide both sides by 4
q = 1
x = 8

9. Questions + - x  Solving Equations (a) 3x + 8 = 20 x = 4
Whatever we do to one side of the equation we must do to the other.
x = 3
Solve the following equations
(a) 3x + 8 = 20
x = 4
(b) 7x - 9 = 26
x = 5
(c) 5x - 40 = - 5
x = 7
(d) 3x + 7 = x + 11
x = 2
(e) 6x + 5 = 4x + 10
x = 2½
(f) 5p - 3 = 2p + 9
p = 4
(g) 4y - 7 = 2y - 9
y = -1
Questions

10. Worksheet (a) 3x + 8 = 20 (a) 3x + 8 = 20 (a) 3x + 8 = 20
(b) 7x - 9 = 26
(b) 7x - 9 = 26
(b) 7x - 9 = 26
(b) 7x - 9 = 26
(c) 5x - 40 = - 5
(c) 5x - 40 = - 5
(c) 5x - 40 = - 5
(c) 5x - 40 = - 5
(d) 3x + 7 = x + 11
(d) 3x + 7 = x + 11
(d) 3x + 7 = x + 11
(d) 3x + 7 = x + 11
(e) 6x + 5 = 4x + 10
(e) 6x + 5 = 4x + 10
(e) 6x + 5 = 4x + 10
(e) 6x + 5 = 4x + 10
(f) 5p - 3 = 2p + 9
(f) 5p - 3 = 2p + 9
(f) 5p - 3 = 2p + 9
(f) 5p - 3 = 2p + 9
(g) 4y - 7 = 2y - 9
(g) 4y - 7 = 2y - 9
(g) 4y - 7 = 2y - 9
(g) 4y - 7 = 2y - 9
Worksheet