Answer:1) To solve the equation 0.1+5(0.3x - 1.5)=15+6.1x, we can start by simplifying both sides of the equation.
On the left side, we need to apply the distributive property to the term 5(0.3x - 1.5). This means we multiply 5 by both terms inside the parentheses:
0.1 + 5(0.3x - 1.5) = 0.1 + (5 * 0.3x - 5 * 1.5)
Simplifying further:
0.1 + (1.5x - 7.5) = 15 + 6.1x
Next, we can combine like terms on both sides of the equation. On the left side, we have 0.1 and -7.5, which can be combined:
(0.1 - 7.5) + 1.5x = 15 + 6.1x
Now, we have -7.4 + 1.5x on the left side, and 15 + 6.1x on the right side.
To isolate the variable x, we want to move all terms with x to one side of the equation and the constant terms to the other side. Let's start by moving the 1.5x term to the right side by subtracting 1.5x from both sides:
-7.4 + 1.5x - 1.5x = 15 + 6.1x - 1.5x
The 1.5x and -1.5x cancel out on the left side, leaving:
-7.4 = 15 + 4.6x
Next, we want to move the constant term 15 to the left side by subtracting 15 from both sides:
-7.4 - 15 = 15 + 4.6x - 15
Simplifying:
-22.4 = 4.6x
Finally, to solve for x, we divide both sides of the equation by 4.6:
-22.4 / 4.6 = 4.6x / 4.6
The result is:
x ≈ -4.87
Therefore, the solution to the equation is x ≈ -4.87.
2) To solve the equation 5x + 17 = 9(3x - 27), we can start by applying the distributive property on the right side:
5x + 17 = 9 * 3x - 9 * 27
Simplifying further:
5x + 17 = 27x - 243
Next, we want to isolate the variable x by moving all terms with x to one side of the equation and the constant terms to the other side. Let's start by subtracting 27x from both sides:
5x + 17 - 27x = 27x - 243 - 27x
Simplifying:
-22x + 17 = -243
Next, we want to move the constant term 17 to the right side by subtracting 17 from both sides:
-22x + 17 - 17 = -243 - 17
Simplifying:
-22x = -260
Finally, to solve for x, we divide both sides of the equation by -22:
-22x / -22 = -260 / -22
The result is:
x = 11.82
Therefore, the solution to the equation is x = 11.82.
Explanation: