Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-6}& = &-4 \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6} & = &-4\color{blue}{+6} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+6}& = &14 \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6} & = &14\color{blue}{-6} \\\Leftrightarrow &14x & = &8\\\Leftrightarrow & \color{red}{14}x & = &8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+12}& = &10 \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12} & = &10\color{blue}{-12} \\\Leftrightarrow &8x & = &-2\\\Leftrightarrow & \color{red}{8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-8}& = &-6 \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8} & = &-6\color{blue}{+8} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+10}& = &14 \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10} & = &14\color{blue}{-10} \\\Leftrightarrow &15x & = &4\\\Leftrightarrow & \color{red}{15}x & = &4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+6}& = &4 \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6} & = &4\color{blue}{-6} \\\Leftrightarrow &-12x & = &-2\\\Leftrightarrow & \color{red}{-12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-3}& = &-9 \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3} & = &-9\color{blue}{+3} \\\Leftrightarrow &4x & = &-6\\\Leftrightarrow & \color{red}{4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+3}& = &3 \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3} & = &3\color{blue}{-3} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+11}& = &-13 \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11} & = &-13\color{blue}{-11} \\\Leftrightarrow &8x & = &-24\\\Leftrightarrow & \color{red}{8}x & = &-24\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-24}{8} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-2}& = &-7 \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2} & = &-7\color{blue}{+2} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+14}& = &-6 \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14} & = &-6\color{blue}{-14} \\\Leftrightarrow &-14x & = &-20\\\Leftrightarrow & \color{red}{-14}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+9}& = &5 \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9} & = &5\color{blue}{-9} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)