Solving the linear equations we have the following solutions:
[tex]a. $ x = -2\\b. $ x = \frac{3}{2} \\c. $ x = 0\\d. $ x = -\frac{1}{5}[/tex]
Each of the equations can be solved as shown below:
a. [tex]3x + 7 = - x - 1[/tex]
[tex]3x + 7 + x = - x - 1 + x[/tex] (addition property of equality)
[tex]4x + 7 = - 1\\4x + 7 - 7 = -1-7[/tex] (Subtraction property of equality)
[tex]4x = -8\\\frac{4x}{4} = \frac{-8}{4}[/tex] (Division property of equality)
[tex]x = -2[/tex]
b. [tex]1 - 2x + 5 = 4x - 3\\[/tex]
Add like terms
[tex]6 - 2x = 4x - 3\\\\6 - 2x - 6 = 4x - 3 - 6[/tex] (Subtraction property of equality)
[tex]- 2x = 4x - 9\\-2x - 4x = 4x -9 - 4x[/tex] (Subtraction property of equality)
[tex]-6x = -9 \\\frac{-6x}{-6} = \frac{-9}{-6}[/tex] (Division property of equality)
[tex]x = \frac{3}{2}[/tex]
c. [tex]4x - 2 + x =-2 + 2x\\[/tex]
[tex]5x - 2 = -2 + 2x\\5x - 2x = -2 + 2\\3x = 0\\ x = \frac{0}{3} \\x = 0[/tex]
d. [tex]3x - 4 + 1 = - 2x -5 + 5x\\[/tex]
[tex]3x - 3 = - 7x -5\\3x + 7x = 3 - 5\\10x = -2\\x = \frac{-2}{10} \\x = -\frac{1}{5}[/tex]
The value of x in each equation are:
[tex]a. $ x = -2\\b. $ x = \frac{3}{2} \\c. $ x = 0\\d. $ x = -\frac{1}{5}[/tex]
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