Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-13}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13-11x } & = & -2 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &-4x & = &11\\\Leftrightarrow & \color{red}{-4}x & = &11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-1}& = & -4 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1-3x } & = & -4 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & -4 \color{blue}{+1} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+4}& = & -2 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4-4x } & = & -2 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & 7x \color{blue}{-4x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &3x & = &-6\\\Leftrightarrow & \color{red}{3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-6}{3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x } & = & -10 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &-5x & = &-6\\\Leftrightarrow & \color{red}{-5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-x } & = & 9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &-10x & = &19\\\Leftrightarrow & \color{red}{-10}x & = &19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-7}& = & -1 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7-6x } & = & -1 \color{red}{ +6x }\color{blue}{+7-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -1 \color{blue}{+7} \\\Leftrightarrow &-x & = &6\\\Leftrightarrow & \color{red}{-}x & = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+7}& = & 9 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7-15x } & = & 9 \color{red}{ +15x }\color{blue}{-7-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-10}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10-8x } & = & -13 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+14}& = & 10 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14+14x } & = & 10 \color{red}{ -14x }\color{blue}{-14+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &29x & = &-4\\\Leftrightarrow & \color{red}{29}x & = &-4\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-4}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{29} } & & \\ & V = \left\{ \frac{-4}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+6}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-14x } & = & 11 \color{red}{ +14x }\color{blue}{-6-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &-23x & = &5\\\Leftrightarrow & \color{red}{-23}x & = &5\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{5}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{23} } & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+9}& = & 10 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9+5x } & = & 10 \color{red}{ -5x }\color{blue}{-9+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 10 \color{blue}{-9} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & 6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)