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Exercise 6 Page 161
a Isolate x on one side and find the number of solutions of the given equation.
b Isolate x on one side and find the number of solutions of the given equation.
c Isolate x on one side and find the number of solutions of the given equation.
d Isolate x on one side and find the number of solutions of the given equation.
e Isolate x on one side and find the number of solutions of the given equation.
f Isolate x on one side and find the number of solutions of the given equation.
a Result: x=8
Clasification: One solution, see solution.
b Result: x=-16/5
Clasification: One solution, see solution.
c No solution, see solution.
d Result: x=2.8
Clasification: One solution, see solution.
e Result: x=-4
Clasification: One solution, see solution.
f Infinitely many solutions, see solution.
Practice makes perfect
a To solve the equation for x, we will use the Properties of Equality to apply inverse operations to both sides of the equation. In this case, we will begin by applying the Subtraction Property of Equality.
2x-9=5x-33
â–¼
Solve for x
SubEqn
LHS-2 x=RHS-2 x
-9=3x-33
AddEqn
LHS+33=RHS+33
24=3x
DivEqn
.LHS /3.=.RHS /3.
8=x
RearrangeEqn
Rearrange equation
x=8
This equation has one solution.
b To solve the equation for x, we will use the Properties of Equality to apply inverse operations to both sides of the equation. In this case, we will begin by applying the Subtraction Property of Equality.
5x-6=10x+10
â–¼
Solve for x
SubEqn
LHS-5 x=RHS-5 x
-6=5x+10
SubEqn
LHS-10=RHS-10
-16=5x
DivEqn
.LHS /5.=.RHS /5.
-16/5=x
RearrangeEqn
Rearrange equation
x=-16/5
This equation has one solution.
c To solve the equation for x, we will begin by applying the Distributive Property to simplify both sides of the equation. Then, we will use the Properties of Equality to apply inverse operations to both sides of the equation.
2(8x-3)=4(4x+7)
0≠34
Because we have reached a contradiction, the equation has no solution.
d To solve the equation for x, we will begin by applying the Distributive Property to simplify the right side of the equation. Then, we will use the Properties of Equality to apply inverse operations to both sides of the equation.
-7x+5=2(x-10.1)
x=2.8
This equation has one solution.
e To solve the equation for x, we will begin by applying the Distributive Property to simplify both sides of the equation. Then, we will use the Properties of Equality to apply inverse operations to both sides of the equation.
6(2x+4)=4(4x+10)
x=-4
This equation has one solution.
f To solve the equation for x, we will begin by applying the Distributive Property to simplify both sides of the equation. Then, we will use the Properties of Equality to apply inverse operations to both sides of the equation.
Because the left-hand side and the right-hand side are the same, we have reached an identity. Therefore, the equation has infinitely many solutions.
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