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Review unit.(4)
1) Solve these equations. Check each of your answers by substituting the
answer back into the equation.
a) 5x+14=-6
b) a-12=5a-2
c) 6(x+2)=4
d) 0 = 12-2(y-3)
64
e)==4
m
f) -
aima Makey 92813874
2) Solve these simultaneous equations using the substitution method.
y=4x-1
3) Solve these simultaneous equations using the elimination method.
x+y=26
x-y=12
4) Solve these inequalities. Check each solution set.
a) 2a+
c) 3(c+5) >2(5c)
b) 5b-1b+ 19
d) 4d ≤ 7d + 15
5) Solve these inequalities. Represent each answer on a number line
a) 3 b) -12 < 3n<3

Sagot :

Réponse :

1) Solve the equations:

a) (5x + 14 = -6)

Solve for (x): [x = \frac{-6 - 14}{5} = -4]

Check: (5(-4) + 14 = -6)

b) (a - 12 = 5a - 2)

Solve for (a): [a = \frac{12 - 2}{5 - 1} = 2]

Check: (2 - 12 = 5(2) - 2)

c) (6(x + 2) = 4)

Solve for (x): [x = \frac{4}{6} - 2 = -\frac{1}{3}]

Check: (6\left(-\frac{1}{3} + 2\right) = 4)

d) (0 = 12 - 2(y - 3))

Solve for (y): [y = \frac{12}{2} + 3 = 9]

Check: (0 = 12 - 2(9 - 3))

e) (\frac{64}{m} = 4)

Solve for (m): [m = \frac{64}{4} = 16]

Check: (\frac{64}{16} = 4)

f) (-\frac{aima}{92813874} = 4)

Solve for (aima): [aima = -4 \times 92813874 = -371255496]

Check: (-\frac{371255496}{92813874} = 4)

2) Solve the simultaneous equations using the substitution method:

Given: [y = 4x - 1]

Substitute (y) into the second equation: [x + (4x - 1) = 26] [5x = 27] [x = \frac{27}{5} = 5.4]

Now find (y): [y = 4(5.4) - 1 = 21.6 - 1 = 20.6]

3) Solve the simultaneous equations using the elimination method:

Given: [x + y = 26] [x - y = 12]

Add the two equations to eliminate (y): [2x = 38] [x = 19]

Now find (y): [y = 26 - x = 26 - 19 = 7]

4) Solve the inequalities:

a) (2a + 3 < 7a)

Solve for (a): [a = \frac{3}{7 - 2} = \frac{3}{5}]

Check: (2\left(\frac{3}{5}\right) + 3 < 7\left(\frac{3}{5}\right))

b) (5b - 1 < b + 19)

Solve for (b): [b = \frac{19 + 1}{5 - 1} = 5]

Check: (5(5) - 1 < 5 + 19)

c) (3(c + 5) > 2(5c))

Solve for (c): [c = \frac{3 \times 5}{2 \times 5 - 3} = 3]

Check: (3(3 + 5) > 2(5 \times 3))

d) (4d \leq 7d + 15)

Solve for (d): [d = \frac{15}{7 - 4} = 5]

Check: (4(5) \leq 7(5) + 15)

5) Represent the inequalities on a number line:

a) (3) b) (-12 < 3n < 3)

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