Math

Question Solve the linear equation 45x+14=86-\frac{4}{5} x + 14 = 86 for the value of xx.

Studdy Solution

STEP 1

Assumptions
1. We have the equation 45x+14=86-\frac{4}{5} x + 14 = 86.
2. We need to solve for xx.

STEP 2

First, we need to isolate the term containing xx on one side of the equation. We can do this by subtracting 14 from both sides of the equation.
45x+1414=8614-\frac{4}{5} x + 14 - 14 = 86 - 14

STEP 3

Perform the subtraction on both sides.
45x=8614-\frac{4}{5} x = 86 - 14

STEP 4

Calculate the result of the subtraction on the right side of the equation.
45x=72-\frac{4}{5} x = 72

STEP 5

Now, we need to solve for xx by getting rid of the fraction 45-\frac{4}{5}. We can do this by multiplying both sides of the equation by the reciprocal of 45-\frac{4}{5}, which is 54-\frac{5}{4}.
54×45x=72×54-\frac{5}{4} \times -\frac{4}{5} x = 72 \times -\frac{5}{4}

STEP 6

On the left side, the reciprocal will cancel out the fraction, leaving us with xx.
x=72×54x = 72 \times -\frac{5}{4}

STEP 7

Now, perform the multiplication on the right side to find the value of xx.
x=72×54x = 72 \times -\frac{5}{4}

STEP 8

Calculate the result of the multiplication.
x=90x = -90
The solution to the equation 45x+14=86-\frac{4}{5} x + 14 = 86 is x=90x = -90.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord