Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-6}& = & 6 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6-10x } & = & 6 \color{red}{ +10x }\color{blue}{+6-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+10}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10-9x } & = & 13 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & 13 \color{blue}{-10} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+2}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & 11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &-12x & = &9\\\Leftrightarrow & \color{red}{-12}x & = &9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3-x } & = & -10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-8}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-5x } & = & 15 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &-7x & = &23\\\Leftrightarrow & \color{red}{-7}x & = &23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+15}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-8x } & = & 5 \color{red}{ +8x }\color{blue}{-15-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-23x & = &-10\\\Leftrightarrow & \color{red}{-23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+5}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5-3x } & = & -15 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &10x & = &-20\\\Leftrightarrow & \color{red}{10}x & = &-20\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-20}{10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-2}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-x } & = & 10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+9}& = & 3 \color{red}{ -5x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9+5x } & = & 3 \color{red}{ -5x }\color{blue}{-9+5x } \\\Leftrightarrow & 13x \color{blue}{+5x } & = & 3 \color{blue}{-9} \\\Leftrightarrow &18x & = &-6\\\Leftrightarrow & \color{red}{18}x & = &-6\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-6}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+2}& = & 3 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2+3x } & = & 3 \color{red}{ -3x }\color{blue}{-2+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &10x & = &1\\\Leftrightarrow & \color{red}{10}x & = &1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+13}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-3x } & = & 1 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &8x & = &-12\\\Leftrightarrow & \color{red}{8}x & = &-12\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-12}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+10}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-x } & = & 10 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)