Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+4}& = &8 \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4} & = &8\color{blue}{-4} \\\Leftrightarrow &15x & = &4\\\Leftrightarrow & \color{red}{15}x & = &4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+15}& = &-11 \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15} & = &-11\color{blue}{-15} \\\Leftrightarrow &-x & = &-26\\\Leftrightarrow & \color{red}{-}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-26}{-1} \\\Leftrightarrow & \color{green}{ x = 26 } & & \\ & V = \left\{ 26 \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-10}& = &14 \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10} & = &14\color{blue}{+10} \\\Leftrightarrow &2x & = &24\\\Leftrightarrow & \color{red}{2}x & = &24\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{24}{2} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-1}& = &-6 \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1} & = &-6\color{blue}{+1} \\\Leftrightarrow &12x & = &-5\\\Leftrightarrow & \color{red}{12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-5}& = &15 \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5} & = &15\color{blue}{+5} \\\Leftrightarrow &-9x & = &20\\\Leftrightarrow & \color{red}{-9}x & = &20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+12}& = &-8 \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12} & = &-8\color{blue}{-12} \\\Leftrightarrow &10x & = &-20\\\Leftrightarrow & \color{red}{10}x & = &-20\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-20}{10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-13}& = &13 \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13} & = &13\color{blue}{+13} \\\Leftrightarrow &14x & = &26\\\Leftrightarrow & \color{red}{14}x & = &26\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{26}{14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-9}& = &-11 \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9} & = &-11\color{blue}{+9} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+11}& = &3 \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11} & = &3\color{blue}{-11} \\\Leftrightarrow &-8x & = &-8\\\Leftrightarrow & \color{red}{-8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-8}{-8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-2}& = &-12 \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2} & = &-12\color{blue}{+2} \\\Leftrightarrow &-6x & = &-10\\\Leftrightarrow & \color{red}{-6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-3}& = &-5 \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3} & = &-5\color{blue}{+3} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+10}& = &9 \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10} & = &9\color{blue}{-10} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)