Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

1. \(-7x+6=8\)
2. \(3x+3=-12\)
3. \(-6x-1=6\)
4. \(6x-13=-12\)
5. \(x-8=-11\)
6. \(2x+4=10\)
7. \(11x-1=10\)
8. \(-13x-1=5\)
9. \(-12x+15=5\)
10. \(13x-7=-6\)
11. \(6x-12=15\)
12. \(-4x+9=13\)

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+6}& = &8 \\\Leftrightarrow & -7x \color{red}{+6}\color{blue}{-6} & = &8\color{blue}{-6} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+3}& = &-12 \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3} & = &-12\color{blue}{-3} \\\Leftrightarrow &3x & = &-15\\\Leftrightarrow & \color{red}{3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-15}{3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-1}& = &6 \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1} & = &6\color{blue}{+1} \\\Leftrightarrow &-6x & = &7\\\Leftrightarrow & \color{red}{-6}x & = &7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-13}& = &-12 \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13} & = &-12\color{blue}{+13} \\\Leftrightarrow &6x & = &1\\\Leftrightarrow & \color{red}{6}x & = &1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-8}& = &-11 \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8} & = &-11\color{blue}{+8} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+4}& = &10 \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4} & = &10\color{blue}{-4} \\\Leftrightarrow &2x & = &6\\\Leftrightarrow & \color{red}{2}x & = &6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{6}{2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-1}& = &10 \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1} & = &10\color{blue}{+1} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-1}& = &5 \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1} & = &5\color{blue}{+1} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+15}& = &5 \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15} & = &5\color{blue}{-15} \\\Leftrightarrow &-12x & = &-10\\\Leftrightarrow & \color{red}{-12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-7}& = &-6 \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7} & = &-6\color{blue}{+7} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-12}& = &15 \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12} & = &15\color{blue}{+12} \\\Leftrightarrow &6x & = &27\\\Leftrightarrow & \color{red}{6}x & = &27\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{27}{6} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+9}& = &13 \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9} & = &13\color{blue}{-9} \\\Leftrightarrow &-4x & = &4\\\Leftrightarrow & \color{red}{-4}x & = &4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{4}{-4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)