To find: The value of K such that the equations

Stefan Hendricks

Stefan Hendricks

Answered question

2021-12-31

To find: The value of K such that the equations x6+4=x3 and x+K=2x are ewuivalent.

Answer & Explanation

Thomas White

Thomas White

Beginner2022-01-01Added 40 answers

Step 1
To solve x6+4=x3
Multiply by 6 on both sides,
6(x6+4)=x3×6
By distributive property ab+ac=a(b+c), the given equation can be simplified as,
6(x6+4)=6×x6+6×
6(x6+4)=1×x+24
6(x6+4)=x+24
Replace 6(x6+4) with x+24
x3×6=x×2
x3×6=2x
Replace x3×6 with 2x
x+24=2x
On comparing x+24=2x and x+K=2x
K=24 The value of K is 24.
Alex Sheppard

Alex Sheppard

Beginner2022-01-02Added 36 answers

Step 1
Given equation: x6+4=x3
Find Least Common Multiplier of 6, 3:6
Multiply by LCM = 6
x6×6+4×6=x3×6
Simplify
x+24=2x
Subtract 24 from both sides
x+2424=2x24
Simplify
x=2x24
Subtract 2x from both sides
x2x=2x242x
Simplify
x=24
Divide both sides by -1
x1=241
Answer: x=24
karton

karton

Expert2022-01-10Added 613 answers

Let's solve your equation step-by-step.
x6+4=x3
Step 1: Simplify both sides of the equation.
16x+4=13x
Step 2: Subtract 13x from both sides
16x+413x=13x13x
16x+4=0
Step 3: Subtract 4 from both sides.
16x+44=04
16x=4
Stpe 4: Multiply both sides by 61
(61)×(16x)=(61)×4
x=24

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