We appreciate your visit to Example 7 Solve the equation tex frac 4m 5 frac 2m 3 4 tex Solution The LCM of 5 and 3 is 15 Multiply both. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To solve the equation
[tex]$$
\frac{4m}{5} - \frac{2m}{3} = 4,
$$[/tex]
follow these steps:
1. Determine the Least Common Multiple (LCM):
The denominators are 5 and 3. Their LCM is 15.
2. Multiply Each Term by 15:
Multiply every term of the equation by 15 to eliminate the fractions:
[tex]$$
15 \times \frac{4m}{5} - 15 \times \frac{2m}{3} = 15 \times 4.
$$[/tex]
Simplify each term:
- For the first term:
[tex]$$
15 \times \frac{4m}{5} = \left(\frac{15}{5}\right) \times 4m = 3 \times 4m = 12m.
$$[/tex]
- For the second term:
[tex]$$
15 \times \frac{2m}{3} = \left(\frac{15}{3}\right) \times 2m = 5 \times 2m = 10m.
$$[/tex]
- For the right-hand side:
[tex]$$
15 \times 4 = 60.
$$[/tex]
The equation now becomes:
[tex]$$
12m - 10m = 60.
$$[/tex]
3. Combine Like Terms and Solve for [tex]$m$[/tex]:
Combine the terms on the left-hand side:
[tex]$$
12m - 10m = 2m,
$$[/tex]
so the equation is:
[tex]$$
2m = 60.
$$[/tex]
Divide both sides by 2 to solve for [tex]$m$[/tex]:
[tex]$$
m = \frac{60}{2} = 30.
$$[/tex]
4. Check the Solution:
Substitute [tex]$m = 30$[/tex] back into the original equation:
[tex]$$
\frac{4(30)}{5} - \frac{2(30)}{3} = \frac{120}{5} - \frac{60}{3} = 24 - 20 = 4.
$$[/tex]
The left-hand side equals the right-hand side, confirming that [tex]$m = 30$[/tex] is the correct solution.
Thus, the solution to the equation is
[tex]$$
m = 30.
$$[/tex]
[tex]$$
\frac{4m}{5} - \frac{2m}{3} = 4,
$$[/tex]
follow these steps:
1. Determine the Least Common Multiple (LCM):
The denominators are 5 and 3. Their LCM is 15.
2. Multiply Each Term by 15:
Multiply every term of the equation by 15 to eliminate the fractions:
[tex]$$
15 \times \frac{4m}{5} - 15 \times \frac{2m}{3} = 15 \times 4.
$$[/tex]
Simplify each term:
- For the first term:
[tex]$$
15 \times \frac{4m}{5} = \left(\frac{15}{5}\right) \times 4m = 3 \times 4m = 12m.
$$[/tex]
- For the second term:
[tex]$$
15 \times \frac{2m}{3} = \left(\frac{15}{3}\right) \times 2m = 5 \times 2m = 10m.
$$[/tex]
- For the right-hand side:
[tex]$$
15 \times 4 = 60.
$$[/tex]
The equation now becomes:
[tex]$$
12m - 10m = 60.
$$[/tex]
3. Combine Like Terms and Solve for [tex]$m$[/tex]:
Combine the terms on the left-hand side:
[tex]$$
12m - 10m = 2m,
$$[/tex]
so the equation is:
[tex]$$
2m = 60.
$$[/tex]
Divide both sides by 2 to solve for [tex]$m$[/tex]:
[tex]$$
m = \frac{60}{2} = 30.
$$[/tex]
4. Check the Solution:
Substitute [tex]$m = 30$[/tex] back into the original equation:
[tex]$$
\frac{4(30)}{5} - \frac{2(30)}{3} = \frac{120}{5} - \frac{60}{3} = 24 - 20 = 4.
$$[/tex]
The left-hand side equals the right-hand side, confirming that [tex]$m = 30$[/tex] is the correct solution.
Thus, the solution to the equation is
[tex]$$
m = 30.
$$[/tex]
Thanks for taking the time to read Example 7 Solve the equation tex frac 4m 5 frac 2m 3 4 tex Solution The LCM of 5 and 3 is 15 Multiply both. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
