Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-1}& = & 2 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1+3x } & = & 2 \color{red}{ -3x }\color{blue}{+1+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &13x & = &3\\\Leftrightarrow & \color{red}{13}x & = &3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-7}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-x } & = & 8 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &-7x & = &15\\\Leftrightarrow & \color{red}{-7}x & = &15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+15}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & -3 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-3}& = & 8 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+6x } & = & 8 \color{red}{ -6x }\color{blue}{+3+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 8 \color{blue}{+3} \\\Leftrightarrow &19x & = &11\\\Leftrightarrow & \color{red}{19}x & = &11\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{11}{19} \\\Leftrightarrow & \color{green}{ x = \frac{11}{19} } & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-11}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11-5x } & = & 10 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-17x & = &21\\\Leftrightarrow & \color{red}{-17}x & = &21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{17} } & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-5}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5+13x } & = & -13 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &23x & = &-8\\\Leftrightarrow & \color{red}{23}x & = &-8\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-8}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{23} } & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+7}& = & 6 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7+13x } & = & 6 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &20x & = &-1\\\Leftrightarrow & \color{red}{20}x & = &-1\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-1}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{20} } & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9-x } & = & -9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &3x & = &-18\\\Leftrightarrow & \color{red}{3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-18}{3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+5}& = & -1 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5+5x } & = & -1 \color{red}{ -5x }\color{blue}{-5+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &16x & = &-6\\\Leftrightarrow & \color{red}{16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-6}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-2}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-5x } & = & -5 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &4x & = &-3\\\Leftrightarrow & \color{red}{4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+13}& = & -7 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13+2x } & = & -7 \color{red}{ -2x }\color{blue}{-13+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &17x & = &-20\\\Leftrightarrow & \color{red}{17}x & = &-20\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-20}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+1}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1+13x } & = & -13 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &12x & = &-14\\\Leftrightarrow & \color{red}{12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-14}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)