Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+11}& = & 13 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+11x } & = & 13 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &15x & = &2\\\Leftrightarrow & \color{red}{15}x & = &2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-x } & = & -11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-26\\\Leftrightarrow & \color{red}{-5}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-26}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{26}{5} } & & \\ & V = \left\{ \frac{26}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-13}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13-9x } & = & 3 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & 11x \color{blue}{-9x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &2x & = &16\\\Leftrightarrow & \color{red}{2}x & = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-5}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5+11x } & = & 4 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &23x & = &9\\\Leftrightarrow & \color{red}{23}x & = &9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+6}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-5x } & = & -15 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -15 \color{blue}{-6} \\\Leftrightarrow &-9x & = &-21\\\Leftrightarrow & \color{red}{-9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-12}& = & 1 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-10x } & = & 1 \color{red}{ +10x }\color{blue}{+12-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &-x & = &13\\\Leftrightarrow & \color{red}{-}x & = &13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{13}{-1} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+6}& = & 1 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6+5x } & = & 1 \color{red}{ -5x }\color{blue}{-6+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &8x & = &-5\\\Leftrightarrow & \color{red}{8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+7}& = & 11 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7+14x } & = & 11 \color{red}{ -14x }\color{blue}{-7+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &19x & = &4\\\Leftrightarrow & \color{red}{19}x & = &4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-10}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-4x } & = & -7 \color{red}{ +4x }\color{blue}{+10-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-4}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-3x } & = & -8 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+15}& = & -9 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15+3x } & = & -9 \color{red}{ -3x }\color{blue}{-15+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &13x & = &-24\\\Leftrightarrow & \color{red}{13}x & = &-24\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-24}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{13} } & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-15}& = & -10 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-6x } & = & -10 \color{red}{ +6x }\color{blue}{+15-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &-17x & = &5\\\Leftrightarrow & \color{red}{-17}x & = &5\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{5}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)