Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+4}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-5x } & = & -11 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+7}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-7x } & = & 4 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &-17x & = &-3\\\Leftrightarrow & \color{red}{-17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+10}& = & -11 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+6x } & = & -11 \color{red}{ -6x }\color{blue}{-10+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &13x & = &-21\\\Leftrightarrow & \color{red}{13}x & = &-21\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-21}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-x } & = & 12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &-13x & = &26\\\Leftrightarrow & \color{red}{-13}x & = &26\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{26}{-13} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+15}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-9x } & = & -13 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-28\\\Leftrightarrow & \color{red}{-13}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-28}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{28}{13} } & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+13}& = & 13 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13-3x } & = & 13 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+6}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-x } & = & 5 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-4}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4+11x } & = & 11 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &26x & = &15\\\Leftrightarrow & \color{red}{26}x & = &15\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{15}{26} \\\Leftrightarrow & \color{green}{ x = \frac{15}{26} } & & \\ & V = \left\{ \frac{15}{26} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+12}& = & 2 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+13x } & = & 2 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &20x & = &-10\\\Leftrightarrow & \color{red}{20}x & = &-10\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-10}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+6}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x } & = & -8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &-6x & = &-14\\\Leftrightarrow & \color{red}{-6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-14}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14-4x } & = & -10 \color{red}{ +4x }\color{blue}{+14-4x } \\\Leftrightarrow & -x \color{blue}{-4x } & = & -10 \color{blue}{+14} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x } & = & 10 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)