Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-15}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15-11x } & = & 13 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 13 \color{blue}{+15} \\\Leftrightarrow &-x & = &28\\\Leftrightarrow & \color{red}{-}x & = &28\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{28}{-1} \\\Leftrightarrow & \color{green}{ x = -28 } & & \\ & V = \left\{ -28 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+6}& = & 1 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+15x } & = & 1 \color{red}{ -15x }\color{blue}{-6+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &19x & = &-5\\\Leftrightarrow & \color{red}{19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-6}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-5x } & = & 15 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &-19x & = &21\\\Leftrightarrow & \color{red}{-19}x & = &21\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{21}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{19} } & & \\ & V = \left\{ \frac{-21}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-3}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x } & = & 6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 6 \color{blue}{+3} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+14}& = & -7 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-6x } & = & -7 \color{red}{ +6x }\color{blue}{-14-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-21\\\Leftrightarrow & \color{red}{-11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+10}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10-5x } & = & -3 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+11}& = & -13 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11+9x } & = & -13 \color{red}{ -9x }\color{blue}{-11+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &19x & = &-24\\\Leftrightarrow & \color{red}{19}x & = &-24\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-24}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{19} } & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+6}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6+13x } & = & 15 \color{red}{ -13x }\color{blue}{-6+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &20x & = &9\\\Leftrightarrow & \color{red}{20}x & = &9\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{9}{20} \\\Leftrightarrow & \color{green}{ x = \frac{9}{20} } & & \\ & V = \left\{ \frac{9}{20} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-5}& = & 15 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5+5x } & = & 15 \color{red}{ -5x }\color{blue}{+5+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &11x & = &20\\\Leftrightarrow & \color{red}{11}x & = &20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x } & = & 1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &-4x & = &-9\\\Leftrightarrow & \color{red}{-4}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-x } & = & -7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+8}& = & 5 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8+15x } & = & 5 \color{red}{ -15x }\color{blue}{-8+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &28x & = &-3\\\Leftrightarrow & \color{red}{28}x & = &-3\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{-3}{28} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{28} } & & \\ & V = \left\{ \frac{-3}{28} \right\} & \\\end{align}\)