Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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