Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-3}& = &15 \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3} & = &15\color{blue}{+3} \\\Leftrightarrow &-10x & = &18\\\Leftrightarrow & \color{red}{-10}x & = &18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+6}& = &2 \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6} & = &2\color{blue}{-6} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-10}& = &12 \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10} & = &12\color{blue}{+10} \\\Leftrightarrow &14x & = &22\\\Leftrightarrow & \color{red}{14}x & = &22\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{22}{14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+5}& = &-14 \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5} & = &-14\color{blue}{-5} \\\Leftrightarrow &-x & = &-19\\\Leftrightarrow & \color{red}{-}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-19}{-1} \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-5}& = &15 \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5} & = &15\color{blue}{+5} \\\Leftrightarrow &-7x & = &20\\\Leftrightarrow & \color{red}{-7}x & = &20\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{20}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-13}& = &-9 \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13} & = &-9\color{blue}{+13} \\\Leftrightarrow &-2x & = &4\\\Leftrightarrow & \color{red}{-2}x & = &4\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{4}{-2} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-2}& = &15 \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2} & = &15\color{blue}{+2} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+15}& = &-9 \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15} & = &-9\color{blue}{-15} \\\Leftrightarrow &5x & = &-24\\\Leftrightarrow & \color{red}{5}x & = &-24\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-24}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{5} } & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+1}& = &2 \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1} & = &2\color{blue}{-1} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+12}& = &5 \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12} & = &5\color{blue}{-12} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+11}& = &2 \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11} & = &2\color{blue}{-11} \\\Leftrightarrow &-2x & = &-9\\\Leftrightarrow & \color{red}{-2}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-9}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-3}& = &-15 \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3} & = &-15\color{blue}{+3} \\\Leftrightarrow &-4x & = &-12\\\Leftrightarrow & \color{red}{-4}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-12}{-4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)