Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{-10}& = &-2 \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10} & = &-2\color{blue}{+10} \\\Leftrightarrow &x & = &8\\\Leftrightarrow & \color{red}{}x & = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+1}& = &5 \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1} & = &5\color{blue}{-1} \\\Leftrightarrow &7x & = &4\\\Leftrightarrow & \color{red}{7}x & = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+7}& = &-9 \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7} & = &-9\color{blue}{-7} \\\Leftrightarrow &5x & = &-16\\\Leftrightarrow & \color{red}{5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+7}& = &9 \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7} & = &9\color{blue}{-7} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+15}& = &-12 \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15} & = &-12\color{blue}{-15} \\\Leftrightarrow &3x & = &-27\\\Leftrightarrow & \color{red}{3}x & = &-27\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-27}{3} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+9}& = &-15 \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9} & = &-15\color{blue}{-9} \\\Leftrightarrow &-4x & = &-24\\\Leftrightarrow & \color{red}{-4}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-24}{-4} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-11}& = &-5 \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11} & = &-5\color{blue}{+11} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+3}& = &-15 \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3} & = &-15\color{blue}{-3} \\\Leftrightarrow &-10x & = &-18\\\Leftrightarrow & \color{red}{-10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-2}& = &-6 \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2} & = &-6\color{blue}{+2} \\\Leftrightarrow &8x & = &-4\\\Leftrightarrow & \color{red}{8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-13}& = &14 \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13} & = &14\color{blue}{+13} \\\Leftrightarrow &-14x & = &27\\\Leftrightarrow & \color{red}{-14}x & = &27\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{27}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{14} } & & \\ & V = \left\{ \frac{-27}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+3}& = &15 \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3} & = &15\color{blue}{-3} \\\Leftrightarrow &-2x & = &12\\\Leftrightarrow & \color{red}{-2}x & = &12\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{12}{-2} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-11}& = &11 \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11} & = &11\color{blue}{+11} \\\Leftrightarrow &15x & = &22\\\Leftrightarrow & \color{red}{15}x & = &22\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{22}{15} \\\Leftrightarrow & \color{green}{ x = \frac{22}{15} } & & \\ & V = \left\{ \frac{22}{15} \right\} & \\\end{align}\)