Sec 1 Mathematics Linear Equations & Inequalities topical questions

Solve each equation.

1. (a)x + 6 = 1[1]
2. (b)4x = -20[1]
3. (c)2x - 5 = 9[1]

Solve (x - 3)/5 = 2.

Write an inequality for each sentence, using x as the number.

1. (a)x is greater than 4.[1]
2. (b)x is at most -2.[1]
3. (c)x is not less than 3.[1]

Solve 6 - 2x = 10 and check your answer by substitution.

Solve each equation.

1. (a)x/5 = −3[1]
2. (b)7x + 4 = 4x + 19[1]
3. (c)2(y + 4) = 12[1]

Solve the inequality 3x + 5 < 20.

Solve 3(x - 2) = 2x + 5.

The sides of a triangle are x cm, (x + 2) cm and 2x cm. Its perimeter is 22 cm.

1. (a)Form an equation in x.[1]
2. (b)Solve the equation.[2]
3. (c)State the length of the shortest side.[1]

Solve the inequality 4x - 3 ≤ 13 and represent the solution on a number line.

At a hawker centre, Wei Ting buys x plates of chicken rice at $3.50 each and one drink at $1.20. Her total bill is $11.70.

1. (a)Form an equation in x.[1]
2. (b)Solve the equation and state how many plates she bought.[2]

A 54 cm wire is bent into a rectangle with length (2x + 1) cm and breadth (x + 2) cm.

1. (a)Form an equation in x.[1]
2. (b)Solve the equation.[2]
3. (c)State the length and breadth of the rectangle.[1]

Solve (2x - 1)/3 = (x + 2)/4.

A gym charges a $9 sign-up fee plus $6 per visit. Mei has a budget of $75 for the gym this term.

1. (a)Write an inequality for the number of visits v she can afford.[1]
2. (b)Solve the inequality.[2]
3. (c)State the greatest number of full visits she can make, with a reason.[1]

Ryan is y years old. His mother is 4 times his age. In 5 years, his mother will be 3 times his age then.

1. (a)Form an equation in y.[2]
2. (b)Solve the equation to find Ryan’s age now.[2]
3. (c)Find his mother’s age now.[1]

Sarah has $m. Her brother has $10 more than twice her amount, and together they have $88.

1. (a)Form an equation in m.[2]
2. (b)Solve the equation for m and state Sarah’s amount.[2]
3. (c)How much more money does her brother have than Sarah?[1]