Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-7}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-x } & = & 5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-15}& = & 5 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-2x } & = & 5 \color{red}{ +2x }\color{blue}{+15-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & 5 \color{blue}{+15} \\\Leftrightarrow &9x & = &20\\\Leftrightarrow & \color{red}{9}x & = &20\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{20}{9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+9}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-7x } & = & -2 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-20x & = &-11\\\Leftrightarrow & \color{red}{-20}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-11}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{20} } & & \\ & V = \left\{ \frac{11}{20} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-x } & = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-10\\\Leftrightarrow & \color{red}{-14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-x } & = & 10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6-x } & = & 11 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &3x & = &5\\\Leftrightarrow & \color{red}{3}x & = &5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+4}& = & 12 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4+7x } & = & 12 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &19x & = &8\\\Leftrightarrow & \color{red}{19}x & = &8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-x } & = & -8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+1}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-5x } & = & -6 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &-19x & = &-7\\\Leftrightarrow & \color{red}{-19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x } & = & -15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-28\\\Leftrightarrow & \color{red}{-13}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-28}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{28}{13} } & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+15}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15-7x } & = & 2 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &8x & = &-13\\\Leftrightarrow & \color{red}{8}x & = &-13\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-13}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-10}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10+11x } & = & -11 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -11 \color{blue}{+10} \\\Leftrightarrow &23x & = &-1\\\Leftrightarrow & \color{red}{23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)