Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-6}& = &15 \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6} & = &15\color{blue}{+6} \\\Leftrightarrow &-3x & = &21\\\Leftrightarrow & \color{red}{-3}x & = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+11}& = &6 \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11} & = &6\color{blue}{-11} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+3}& = &-2 \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3} & = &-2\color{blue}{-3} \\\Leftrightarrow &4x & = &-5\\\Leftrightarrow & \color{red}{4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-11}& = &-13 \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11} & = &-13\color{blue}{+11} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+11}& = &9 \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11} & = &9\color{blue}{-11} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+1}& = &7 \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1} & = &7\color{blue}{-1} \\\Leftrightarrow &2x & = &6\\\Leftrightarrow & \color{red}{2}x & = &6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{6}{2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+11}& = &8 \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11} & = &8\color{blue}{-11} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+2}& = &9 \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2} & = &9\color{blue}{-2} \\\Leftrightarrow &15x & = &7\\\Leftrightarrow & \color{red}{15}x & = &7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-5}& = &12 \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5} & = &12\color{blue}{+5} \\\Leftrightarrow &9x & = &17\\\Leftrightarrow & \color{red}{9}x & = &17\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{17}{9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+12}& = &15 \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12} & = &15\color{blue}{-12} \\\Leftrightarrow &9x & = &3\\\Leftrightarrow & \color{red}{9}x & = &3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+13}& = &6 \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13} & = &6\color{blue}{-13} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-2}& = &-11 \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2} & = &-11\color{blue}{+2} \\\Leftrightarrow &5x & = &-9\\\Leftrightarrow & \color{red}{5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)