Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+2}& = &-13 \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2} & = &-13\color{blue}{-2} \\\Leftrightarrow &-2x & = &-15\\\Leftrightarrow & \color{red}{-2}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-15}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{15}{2} } & & \\ & V = \left\{ \frac{15}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-4}& = &1 \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4} & = &1\color{blue}{+4} \\\Leftrightarrow &7x & = &5\\\Leftrightarrow & \color{red}{7}x & = &5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-13}& = &-2 \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13} & = &-2\color{blue}{+13} \\\Leftrightarrow &x & = &11\\\Leftrightarrow & \color{red}{}x & = &11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 11 \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-9}& = &-5 \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9} & = &-5\color{blue}{+9} \\\Leftrightarrow &4x & = &4\\\Leftrightarrow & \color{red}{4}x & = &4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{4}{4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-1}& = &13 \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1} & = &13\color{blue}{+1} \\\Leftrightarrow &-13x & = &14\\\Leftrightarrow & \color{red}{-13}x & = &14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-15}& = &-4 \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15} & = &-4\color{blue}{+15} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-4}& = &-13 \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4} & = &-13\color{blue}{+4} \\\Leftrightarrow &9x & = &-9\\\Leftrightarrow & \color{red}{9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-9}{9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-6}& = &5 \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6} & = &5\color{blue}{+6} \\\Leftrightarrow &-2x & = &11\\\Leftrightarrow & \color{red}{-2}x & = &11\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{11}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+5}& = &10 \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5} & = &10\color{blue}{-5} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+6}& = &-6 \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6} & = &-6\color{blue}{-6} \\\Leftrightarrow &8x & = &-12\\\Leftrightarrow & \color{red}{8}x & = &-12\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-12}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+7}& = &2 \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7} & = &2\color{blue}{-7} \\\Leftrightarrow &3x & = &-5\\\Leftrightarrow & \color{red}{3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+13}& = &8 \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13} & = &8\color{blue}{-13} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)