Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-5}& = &9 \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5} & = &9\color{blue}{+5} \\\Leftrightarrow &9x & = &14\\\Leftrightarrow & \color{red}{9}x & = &14\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{14}{9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-9}& = &-11 \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9} & = &-11\color{blue}{+9} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+11}& = &15 \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11} & = &15\color{blue}{-11} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+8}& = &-1 \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8} & = &-1\color{blue}{-8} \\\Leftrightarrow &-2x & = &-9\\\Leftrightarrow & \color{red}{-2}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-9}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-9}& = &11 \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9} & = &11\color{blue}{+9} \\\Leftrightarrow &-11x & = &20\\\Leftrightarrow & \color{red}{-11}x & = &20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-10}& = &10 \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10} & = &10\color{blue}{+10} \\\Leftrightarrow &5x & = &20\\\Leftrightarrow & \color{red}{5}x & = &20\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{20}{5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-11}& = &7 \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11} & = &7\color{blue}{+11} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-6}& = &12 \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6} & = &12\color{blue}{+6} \\\Leftrightarrow &8x & = &18\\\Leftrightarrow & \color{red}{8}x & = &18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+10}& = &10 \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10} & = &10\color{blue}{-10} \\\Leftrightarrow &4x & = &0\\\Leftrightarrow & \color{red}{4}x & = &0\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{0}{4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+5}& = &-7 \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5} & = &-7\color{blue}{-5} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+8}& = &13 \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8} & = &13\color{blue}{-8} \\\Leftrightarrow &-10x & = &5\\\Leftrightarrow & \color{red}{-10}x & = &5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-8}& = &4 \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8} & = &4\color{blue}{+8} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)