Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

1. \(-6x+2=-6\)
2. \(-15x-8=-9\)
3. \(8x+5=-13\)
4. \(-15x+1=10\)
5. \(-5x+7=-2\)
6. \(-14x+10=12\)
7. \(5x-2=11\)
8. \(6x+12=9\)
9. \(7x+13=10\)
10. \(8x-2=2\)
11. \(x-12=-3\)
12. \(-15x+11=-14\)

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+2}& = &-6 \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2} & = &-6\color{blue}{-2} \\\Leftrightarrow &-6x & = &-8\\\Leftrightarrow & \color{red}{-6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-8}& = &-9 \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8} & = &-9\color{blue}{+8} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+5}& = &-13 \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5} & = &-13\color{blue}{-5} \\\Leftrightarrow &8x & = &-18\\\Leftrightarrow & \color{red}{8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+1}& = &10 \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1} & = &10\color{blue}{-1} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+7}& = &-2 \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7} & = &-2\color{blue}{-7} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+10}& = &12 \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10} & = &12\color{blue}{-10} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-2}& = &11 \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2} & = &11\color{blue}{+2} \\\Leftrightarrow &5x & = &13\\\Leftrightarrow & \color{red}{5}x & = &13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+12}& = &9 \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12} & = &9\color{blue}{-12} \\\Leftrightarrow &6x & = &-3\\\Leftrightarrow & \color{red}{6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+13}& = &10 \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13} & = &10\color{blue}{-13} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-2}& = &2 \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2} & = &2\color{blue}{+2} \\\Leftrightarrow &8x & = &4\\\Leftrightarrow & \color{red}{8}x & = &4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-12}& = &-3 \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12} & = &-3\color{blue}{+12} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+11}& = &-14 \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11} & = &-14\color{blue}{-11} \\\Leftrightarrow &-15x & = &-25\\\Leftrightarrow & \color{red}{-15}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-25}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)