Exercise 50 Page 65

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To solve the equation for x, we should isolate x on one side of the equation by performing inverse operations.

2x+8=3x-4

SubEqn

LHS-3x=RHS-3x

- x+8=-4

SubEqn

LHS-8=RHS-8

- x=-12

MultEqn

LHS * (- 1)=RHS* (- 1)

x=12

We can check the solution by substituting x=12 in the original equation. If the left-hand side and right-hand side are equal, the solution is correct.

2x+8=3x-4

Substitute

x= 12

2( 12)+8 ? =3( 12)-4

Multiply

24+8? =36-4

AddSubTerms

Add and subtract terms

32=32

The solution is correct.

Like in Part A, to solve this equation we have to isolate w on one side of the equation by performing inverse operations.

1.5w+3=3+2w

SubEqn

LHS-2w=RHS-2w

-0.5w+3=3

SubEqn

LHS-3=RHS-3

-0.5w=0

MultEqn

LHS * (- 1)=RHS* (- 1)

0.5w=0

DivEqn

.LHS /0.5.=.RHS /0.5.

w=0

We will check our solution by substituting it into the original equation.

1.5w+3=3+2w

Substitute

w= 0

1.5( 0)+3? =3+2( 0)

Multiply

0+3? =3+0

AddTerms

Add terms

0=0

The solution is correct.

Like in Parts A and B, we will isolate x by performing inverse operations.

48+8x+23=7

SimpTerms

Simplify terms

71+8x=7

SubEqn

LHS-71=RHS-71

8x=-64

DivEqn

.LHS /8.=.RHS /8.

x=- 8

We will check our solution by substituting it into the original equation.

48+8x+23=7

Substitute

x= -8

48+8( -8)+23? =7

Multiply

48-64+23? =7

AddSubTerms

Add and subtract terms

7=7

The solution is correct.

Like in previous parts, we will try to solve the equation by performing inverse operations.

6x-21=5x+17+x

AddTerms

Add terms

6x-21=6x+17

SubEqn

LHS-6x=RHS-6x

-21≠ 17

When trying to solve the equation we reached a contradiction, which means this equation has no solution.

Subchapter links

2.2.1 Slope as Motion p.64-65

2.2.2 Rate of Change p.70-71

2.2.3 Equations of Lines in Situations p.74-75

Exercise 50 Page 65

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