Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-5}& = &-10 \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5} & = &-10\color{blue}{+5} \\\Leftrightarrow &4x & = &-5\\\Leftrightarrow & \color{red}{4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-7}& = &-8 \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7} & = &-8\color{blue}{+7} \\\Leftrightarrow &6x & = &-1\\\Leftrightarrow & \color{red}{6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-4}& = &-13 \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4} & = &-13\color{blue}{+4} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-15}& = &3 \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15} & = &3\color{blue}{+15} \\\Leftrightarrow &6x & = &18\\\Leftrightarrow & \color{red}{6}x & = &18\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{18}{6} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-10}& = &13 \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10} & = &13\color{blue}{+10} \\\Leftrightarrow &-11x & = &23\\\Leftrightarrow & \color{red}{-11}x & = &23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-12}& = &6 \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12} & = &6\color{blue}{+12} \\\Leftrightarrow &4x & = &18\\\Leftrightarrow & \color{red}{4}x & = &18\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{18}{4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-10}& = &8 \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10} & = &8\color{blue}{+10} \\\Leftrightarrow &-13x & = &18\\\Leftrightarrow & \color{red}{-13}x & = &18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-4}& = &2 \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4} & = &2\color{blue}{+4} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-12}& = &-7 \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12} & = &-7\color{blue}{+12} \\\Leftrightarrow &9x & = &5\\\Leftrightarrow & \color{red}{9}x & = &5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-15}& = &-12 \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15} & = &-12\color{blue}{+15} \\\Leftrightarrow &5x & = &3\\\Leftrightarrow & \color{red}{5}x & = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+4}& = &2 \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4} & = &2\color{blue}{-4} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+9}& = &-10 \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9} & = &-10\color{blue}{-9} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)