There are 4 problems that I don't understand how to solve so, please help me. A numerical explanation with words explanation would be nice. Thank you tutors.
Rewrite each equation so it is in the form ax + b = c or x + d/e = f, where x is a variable. Then solve the equation.
1. 6 + 5x - 1/3 = 10
2. 7 + 3 - 4x/5 = 0
In each equation, one of the letters represents a variable and the other letters represent constants. Solve for the indicated variable and describe what operations you performed to solve for the variable.
3. Solve rs + t = u for the variable s.
4. Solve n + m/p = q for the variable n.
1.
5 x - 1/3 = 4
2.
(4/5) x - 3 = 7
3.
r s = u - t
s = (u-t)/r
4.
n = q - m/p
Thank you tutor Damon. I still don't understand, for the equation you gave me for #2, I got x = 12.5 and when I check it, 3 - 50 = -47/5 = -9.4 + 7 = -2.4 and not 0. For #3 and 4, I still don't understand how to solve it.
2.
(4/5) x = 10
4 x = 50
x = 12.5
------------
check
10 - (4/5)12.5
10 - 50/5
10 - 10
0 yes
Sure! I'll help you solve each problem step by step and explain the process along the way.
1. To rewrite the equation 6 + 5x - 1/3 = 10 in the form ax + b = c:
First, let's move the constant term (-1/3) to the other side of the equation by subtracting it from both sides:
6 + 5x - 1/3 - 1/3 = 10 - 1/3
Simplifying on both sides:
6 + 5x - 2/3 = 30/3 - 1/3
6 + 5x - 2/3 = 29/3
To further simplify, let's find a common denominator and combine the fractions on the left side:
Multiplying the numerator and denominator of 2/3 by 3, we get 6/9:
6 + 5x - 6/9 = 29/3
Now, combine like terms on the left side:
(6 - 6/9) + 5x = 29/3
To get a common denominator on the left side, multiply the numerator and denominator of 6/9 by 3:
(6 * 3/9) + 5x = 29/3
18/9 + 5x = 29/3
Simplifying further, we have:
2 + 5x = 29/3
Now, subtract 2 from both sides to isolate the variable term:
2 - 2 + 5x = 29/3 - 2
5x = 23/3
Finally, to solve for x, divide both sides of the equation by 5:
(5x)/5 = (23/3)/5
x = 23/15
So the solution to the equation is x = 23/15.
2. Let's rewrite the equation 7 + 3 - 4x/5 = 0 in the form x + d/e = f:
First, let's simplify the equation:
10 - 4x/5 = 0
To eliminate the fraction, multiply both sides by 5:
5 * (10 - 4x/5) = 5 * 0
50 - 4x = 0
Next, subtract 50 from both sides to isolate the variable term:
50 - 4x - 50 = 0 - 50
-4x = -50
Now, divide both sides by -4 to solve for x:
(-4x)/(-4) = (-50)/(-4)
x = 50/4
Simplifying further, we have:
x = 25/2
So the solution to the equation is x = 25/2.
3. For the equation rs + t = u, we need to solve for the variable s.
To solve for s, let's isolate the variable by subtracting t from both sides of the equation:
rs + t - t = u - t
rs = u - t
Now, divide both sides of the equation by r to solve for s:
(rs)/r = (u - t)/r
s = (u - t)/r
So the solution for s is s = (u - t)/r.
4. For the equation n + m/p = q, we need to solve for the variable n.
To solve for n, let's isolate the variable by subtracting m/p from both sides of the equation:
n + m/p - m/p = q - m/p
n = q - m/p
So the solution for n is n = q - m/p.
I hope this explanation helps you understand how to solve these types of equations and shows you the step-by-step process involved in rewriting equations and isolating variables. If you have any further questions, feel free to ask!