Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+15}& = &-8 \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15} & = &-8\color{blue}{-15} \\\Leftrightarrow &-3x & = &-23\\\Leftrightarrow & \color{red}{-3}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-23}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{23}{3} } & & \\ & V = \left\{ \frac{23}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+15}& = &2 \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15} & = &2\color{blue}{-15} \\\Leftrightarrow &-15x & = &-13\\\Leftrightarrow & \color{red}{-15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+5}& = &4 \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5} & = &4\color{blue}{-5} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+15}& = &10 \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15} & = &10\color{blue}{-15} \\\Leftrightarrow &8x & = &-5\\\Leftrightarrow & \color{red}{8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+6}& = &14 \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6} & = &14\color{blue}{-6} \\\Leftrightarrow &14x & = &8\\\Leftrightarrow & \color{red}{14}x & = &8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+6}& = &3 \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6} & = &3\color{blue}{-6} \\\Leftrightarrow &9x & = &-3\\\Leftrightarrow & \color{red}{9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+2}& = &15 \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2} & = &15\color{blue}{-2} \\\Leftrightarrow &9x & = &13\\\Leftrightarrow & \color{red}{9}x & = &13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+15}& = &-6 \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15} & = &-6\color{blue}{-15} \\\Leftrightarrow &-10x & = &-21\\\Leftrightarrow & \color{red}{-10}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-21}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{21}{10} } & & \\ & V = \left\{ \frac{21}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+15}& = &3 \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15} & = &3\color{blue}{-15} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+5}& = &14 \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5} & = &14\color{blue}{-5} \\\Leftrightarrow &-2x & = &9\\\Leftrightarrow & \color{red}{-2}x & = &9\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{9}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-14}& = &-1 \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14} & = &-1\color{blue}{+14} \\\Leftrightarrow &15x & = &13\\\Leftrightarrow & \color{red}{15}x & = &13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+6}& = &-5 \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6} & = &-5\color{blue}{-6} \\\Leftrightarrow &14x & = &-11\\\Leftrightarrow & \color{red}{14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-11}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)