Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+6}& = & -2 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-14x } & = & -2 \color{red}{ +14x }\color{blue}{-6-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &-27x & = &-8\\\Leftrightarrow & \color{red}{-27}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-8}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{8}{27} } & & \\ & V = \left\{ \frac{8}{27} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+7}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-x } & = & -1 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1-x } & = & -11 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &14x & = &-10\\\Leftrightarrow & \color{red}{14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-10}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+7}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7+7x } & = & 2 \color{red}{ -7x }\color{blue}{-7+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &15x & = &-5\\\Leftrightarrow & \color{red}{15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & 11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+13}& = & 13 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13+7x } & = & 13 \color{red}{ -7x }\color{blue}{-13+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &19x & = &0\\\Leftrightarrow & \color{red}{19}x & = &0\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{0}{19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-6}& = & 3 \color{red}{ -5x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6+5x } & = & 3 \color{red}{ -5x }\color{blue}{+6+5x } \\\Leftrightarrow & 13x \color{blue}{+5x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &18x & = &9\\\Leftrightarrow & \color{red}{18}x & = &9\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{9}{18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-14}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-x } & = & 13 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &-12x & = &27\\\Leftrightarrow & \color{red}{-12}x & = &27\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{27}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-6}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-x } & = & -1 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &-6x & = &5\\\Leftrightarrow & \color{red}{-6}x & = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+2}& = & -9 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2+6x } & = & -9 \color{red}{ -6x }\color{blue}{-2+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &19x & = &-11\\\Leftrightarrow & \color{red}{19}x & = &-11\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-11}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{19} } & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+15}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-x } & = & 2 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &-4x & = &-13\\\Leftrightarrow & \color{red}{-4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+10}& = & 5 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10+13x } & = & 5 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 5 \color{blue}{-10} \\\Leftrightarrow &27x & = &-5\\\Leftrightarrow & \color{red}{27}x & = &-5\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-5}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{27} } & & \\ & V = \left\{ \frac{-5}{27} \right\} & \\\end{align}\)