1). 7 = z/4
2). -7 = 9 - 7
3). t/6 = -7
4). 20 = x - 3x
5). 5/6x - 1/3 = 5/2
6). (29.5 - 7)/ 1.25
7). 2/3 = 4j/ 6
My answers to these questions are the following:
1). z = 28
2). q = 0
3). t = -42
4). ?
5). ?
6). ?
7). ?
1 and 3 are right. 2???
4).
20 = x - 3x
20 = -2x
-10 = x
5.
5/6x - 1/3 = 5/2
5/6x = 5/2 + 1/3
5/6x = 15/6 + 2/6
5/6x = 17/6
x = (17/6) / (5/6)
x = (17/6) * (6/5)
x = 102/30 = 3 2/5
You can try the last two yourself. I'll be glad to check your answers.
#2. ? where did q come from?
#4 x = -10
#5 x = 17/5
#6 18
#7 j = 1
Let's go through each of these equations step by step and solve for the unknown variable.
1) 7 = z/4
To find z, we can multiply both sides of the equation by 4:
7*4 = z/4 * 4
28 = z
So, z = 28.
2) -7 = 9 - 7
To find q, we need to isolate it on one side of the equation. By subtracting 9 from both sides:
-7 - 9 = 9 - 7 - 9
-16 = q
So, q = -16.
3) t/6 = -7
To find t, we can multiply both sides of the equation by 6:
(t/6) * 6 = -7 * 6
t = -42
So, t = -42.
4) 20 = x - 3x
To find x, we need to combine like terms on the right side of the equation:
20 = x - 3x
20 +2x = x +2x -3x (Here we added 2x to both sides to solve for x)
20 +2x = -x
20 + 2x + x = -x + x
20 + 3x = 0
3x = -20
x = -20/3
So, x = -20/3.
5) 5/6x - 1/3 = 5/2
To solve for x, we need to first eliminate the fractions. We can do this by finding a common denominator, which is 6:
Multiply the first term by 3/3 and the second term by 2/2 to get rid of the fractions:
(5/6x)(3/3) - (1/3)(2/2) = (5/2)(3/3)
15/18x - 2/6 = 15/6
Next, simplify the equation:
15x/18 - 2/6 = 15/6
To get rid of the denominators, we can multiply every term by 18:
18*(15x/18) - 18*(2/6) = 18*(15/6)
Canceling out the denominators, we have:
15x - 6 = 45
Now, isolate x by subtracting 6 from both sides:
15x - 6 - 6 = 45 - 6
15x = 39
Finally, divide both sides by 15 to solve for x:
x = 39/15
So, x = 13/5.
6) (29.5 - 7)/ 1.25
To solve for this expression, divide the numerator by the denominator:
(29.5 - 7) / 1.25 = 22.5 / 1.25
Now, divide 22.5 by 1.25 to get the result:
22.5 / 1.25 = 18
So, the answer is 18.
7) 2/3 = 4j/6
To find j, we need to cross-multiply and solve for j. Multiply the numerator of the first fraction with the denominator of the second fraction and the numerator of the second fraction with the denominator of the first fraction:
(2)(6) = (4j)(3)
12 = 12j
Now, divide both sides of the equation by 12 to solve for j:
12/12 = 12j/12
1 = j
So, j = 1.
Therefore, the correct answers to the equations are:
1) z = 28
2) q = -16
3) t = -42
4) x = -20/3
5) x = 13/5
6) Result is 18 (no variable involved)
7) j = 1.