Download Topic 3: Linear Equations and Inequalities Solving a linear equation

Topic 3: Linear Equations and Inequalities
Solving a linear equation in one variable. Solve.
1. 3x – 7 = 6x + 11
2
2. x = 3x – 1
Solve for the indicated variable in terms of the other(s).
3. P = 2l + 2w
l=
2
T=
4. R = 3(T – 6)
Solution of a one variable equation reducible to a linear equation. Solve and check.
5.
6.
𝑥−1
𝑥+ 3
𝑛
𝑛−4
7
7. |4 − 2𝑧| = 6
=3
8. |𝑥 + 5| = -3
=7
Solution of linear inequalities. Solve.
9. 7 – 2x ≤ 11
10. –3m + 2 > 20
11. 8y – 13 ≥ 4y + 3
Solving a pair of linear equations in two variables. Solve.
12. x + y = 9
𝑦
x–3=1
13. 2x – 3y = –1
9y = 6x + 3
14. 7x + 4 = y
2y – 14x = –8
ANSWERS:
1. x = –6
2. x = –3
3. l =
𝑃−2𝑤
3
2
𝑃
or l = 2 – w
4. T = 2 R + 6
5. x = –6
6. n =
14
3
2
or 43
7. z = –1 or z = 5
8. no solution
9. x ≥ –2
10. m < –6
11. y ≥ 4
12. (3,6)
13. There are infinitely many solutions because the lines are actually the same. The
solution set to describe all solutions is { (x,y) | 2x – 3y = – 1} or { (x,y) | 9y = 6x + 3}
14. There is no solution. The solution set to describe all solutions is empty: { } or Ø.
For more examples, click here