Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+14}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14+11x } & = & 4 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &20x & = &-10\\\Leftrightarrow & \color{red}{20}x & = &-10\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-10}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-6}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-x } & = & -2 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -2 \color{blue}{+6} \\\Leftrightarrow &11x & = &4\\\Leftrightarrow & \color{red}{11}x & = &4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+12}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12-x } & = & -5 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -5 \color{blue}{-12} \\\Leftrightarrow &3x & = &-17\\\Leftrightarrow & \color{red}{3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+13}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13+11x } & = & -7 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &17x & = &-20\\\Leftrightarrow & \color{red}{17}x & = &-20\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-20}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-15}& = & 12 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-4x } & = & 12 \color{red}{ +4x }\color{blue}{+15-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &-11x & = &27\\\Leftrightarrow & \color{red}{-11}x & = &27\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{27}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{11} } & & \\ & V = \left\{ \frac{-27}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+6}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-7x } & = & 5 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-20x & = &-1\\\Leftrightarrow & \color{red}{-20}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-1}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{20} } & & \\ & V = \left\{ \frac{1}{20} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+2}& = & 8 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2+8x } & = & 8 \color{red}{ -8x }\color{blue}{-2+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &7x & = &6\\\Leftrightarrow & \color{red}{7}x & = &6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-14}& = & 15 \color{red}{ +14x } \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14-14x } & = & 15 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & x \color{blue}{-14x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &-13x & = &29\\\Leftrightarrow & \color{red}{-13}x & = &29\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{29}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{13} } & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-2}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2-x } & = & 13 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 13 \color{blue}{+2} \\\Leftrightarrow &11x & = &15\\\Leftrightarrow & \color{red}{11}x & = &15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-5}& = & -6 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-12x } & = & -6 \color{red}{ +12x }\color{blue}{+5-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -6 \color{blue}{+5} \\\Leftrightarrow &-23x & = &-1\\\Leftrightarrow & \color{red}{-23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-10}& = & -3 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10-12x } & = & -3 \color{red}{ +12x }\color{blue}{+10-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+4}& = & 11 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4+7x } & = & 11 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 11 \color{blue}{-4} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)