Answer:
Step-by-step explanation:
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Linear Equation Problems
Value of the unknown quantity for which from given equation we get true numerical equality is called root of that equation. Two equations are called equivalent when the multitudes of their roots match, the roots of the first equation are also roots of the second and vice versa. The following rules are valid:
1. If in given equation one expression is substituted with another identity one, we get equation equivalent to the given.
2. If in given equation some expression is transferred from one side to the other with contrary sign, we get equation equivalent to the given.
3. If we multiply or divide both sides of given equation with the same number, different from zero, we get equation equivalent to the given.
Equation of the kind \displaystyle ax + b = 0ax+b=0, where \displaystyle a, ba,b are given numbers is called simple equation in reference to the unknown quantity \displaystyle xx.
Problem 1 Solve the equation:
A) 16x + 10 – 32 = 35 – 10x - 5
B) \displaystyle y + \frac{3}{2y} + 25 = \frac{1}{2}y + \frac{3}{4}y – \frac{5}{2}y + y + 37y+
2y
3
+25=
2
1
y+
4
3
y–
2
5
y+y+37
C) 7u – 9 – 3u + 5 = 11u – 6 – 4u
Solution:
A)We do some of the makred actions and we get
16x – 22 = 30 – 10x
After using rule 2 we find 16x + 10x = 30 + 22
After doing the addition 26x = 52
We find unknown multiplier by dividing the product by the other multiplier.
That is why \displaystyle x = \frac{52}{26}x=
26
52
Therefore x = 2
B) By analogy with A) we find:
\displaystyle y\left(1 + \frac{3}{2}\right) + 25 = y\left(\frac{1}{2} + \frac{3}{4} – \frac{5}{2} + 1\right) + 37 \Leftrightarrowy(1+
2
3
)+25=y(
2
1
+
4
3
–
2
5
+1)+37⇔
\displaystyle \frac{5}{2}y + 25 = -\frac{1}{4}y + 37 \Leftrightarrow \frac{5}{2}y + \frac{1}{4}y = 37 - 25 \Leftrightarrow
2
5
y+25=−
4
1
y+37⇔
2
5
y+
4
1
y=37−25⇔
\displaystyle \frac{11}{4}y = 12 \Leftrightarrow y = \frac{12.4}{11} \Leftrightarrow y = \frac{48}{11}
4
11
y=12⇔y=
11
12.4
⇔y=
11
48
C) 4u – 4 = 7u – 6 <=> 6 – 4 = 7u – 4u <=> 2 = 3u <=> \displaystyle u = \frac{2}{3}u=
3
2
