Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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