1) 2x - a = 4 - 5x;
2) 3(x - a) = 2(4 - x);
3) 2(x + a) = 8 - a + x;
4) 3(x - a) = 4 - 5a + x.
1) 2(a - x) = a + 2 - 4x;
2) 3(x - 2a) = 2x + a - 3;
3) 5(4a - x) = 7(2 - x);
4) 3(2a - 3x) = 2(3 - x).
1) 3(x + a) = 2 - x, x > 2;
2) 5(a - x) = 3 + 2a, x < 1;
3) 3(3a - 2x) = 12a - 2, x < 3;
4) 5(2a + 3x) = 6a + 4, x < 1.
1) 5(10 - a) x^2 - 10x + 6 - a = 0;
2) (a - 3) x^2 - 2(3a - 4) x + 7a - 6 = 0;
3) 5(a + 4) x^2 - 10x + a = 0;
4) a x^2 + 2(a + 1) x - 2a - 1 = 0.
2) (a^2 - 9) x = a^2 + 2a - 3.
Answer (2)
Let's solve each of the given equations step-by-step:
Equation 1: 2 x − a = 4 − 5 x
To solve for x , we'll first get all the terms involving x on one side:
2 x + 5 x = a + 4
Combine like terms:
7 x = a + 4
Now, solve for x by dividing both sides by 7:
x = 7 a + 4
Equation 2: 3 ( x − a ) = 2 ( 4 − x )
Distribute on both sides:
3 x − 3 a = 8 − 2 x
Add 2 x to both sides:
3 x + 2 x − 3 a = 8
Combine like terms:
5 x − 3 a = 8
Rearrange and solve for x :
5 x = 3 a + 8
x = 5 3 a + 8
Equation 3: 2 ( x + a ) = 8 − a + x
Distribute 2 on the left-hand side:
2 x + 2 a = 8 − a + x
Get all x terms on one side and constants on the other:
2 x − x = 8 − a − 2 a
Combine terms:
x = 8 − 3 a
Equation 4: 3 ( x − a ) = 4 − 5 a + x
Distribute 3 on the left-hand side:
3 x − 3 a = 4 − 5 a + x
Bring all x terms to one side:
3 x − x = 4 − 5 a + 3 a
Combine terms:
2 x = 4 − 2 a
Solve for x :
x = 2 4 − 2 a
x = 2 − a
Each equation involves solving for x in terms of a , using fundamental algebraic operations such as distributing, combining like terms, and isolating x on one side. Understanding these concepts is crucial in high school algebra.
We solved four algebraic equations involving the variable x and the parameter a, demonstrating techniques like distribution and combining like terms. The solutions we found for x in terms of a are: x = (a + 4)/7, x = (3a + 8)/5, x = 8 - 3a, and x = 2 - a. Mastering these methods will strengthen your understanding of algebra.
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