Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-12}& = &-9 \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12} & = &-9\color{blue}{+12} \\\Leftrightarrow &3x & = &3\\\Leftrightarrow & \color{red}{3}x & = &3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{3}{3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-2}& = &6 \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2} & = &6\color{blue}{+2} \\\Leftrightarrow &9x & = &8\\\Leftrightarrow & \color{red}{9}x & = &8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-4}& = &3 \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4} & = &3\color{blue}{+4} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-8}& = &-2 \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8} & = &-2\color{blue}{+8} \\\Leftrightarrow &10x & = &6\\\Leftrightarrow & \color{red}{10}x & = &6\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{6}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+5}& = &5 \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5} & = &5\color{blue}{-5} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-15}& = &-2 \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15} & = &-2\color{blue}{+15} \\\Leftrightarrow &2x & = &13\\\Leftrightarrow & \color{red}{2}x & = &13\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{13}{2} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+9}& = &9 \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9} & = &9\color{blue}{-9} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+11}& = &5 \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11} & = &5\color{blue}{-11} \\\Leftrightarrow &-2x & = &-6\\\Leftrightarrow & \color{red}{-2}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-6}{-2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+2}& = &-7 \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2} & = &-7\color{blue}{-2} \\\Leftrightarrow &10x & = &-9\\\Leftrightarrow & \color{red}{10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-9}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-15}& = &4 \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15} & = &4\color{blue}{+15} \\\Leftrightarrow &x & = &19\\\Leftrightarrow & \color{red}{}x & = &19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 19 \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+10}& = &10 \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10} & = &10\color{blue}{-10} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-1}& = &-4 \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1} & = &-4\color{blue}{+1} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)