Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+13}& = & 15 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13+8x } & = & 15 \color{red}{ -8x }\color{blue}{-13+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+3}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-x } & = & 14 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+1}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1-8x } & = & -13 \color{red}{ +8x }\color{blue}{-1-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &x & = &-14\\\Leftrightarrow & \color{red}{}x & = &-14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -14 \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+1}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1-11x } & = & -9 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-6x & = &-10\\\Leftrightarrow & \color{red}{-6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-14}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & -15 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{+14} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-14}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-4x } & = & -1 \color{red}{ +4x }\color{blue}{+14-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &-11x & = &13\\\Leftrightarrow & \color{red}{-11}x & = &13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-7}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7-7x } & = & -10 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -10 \color{blue}{+7} \\\Leftrightarrow &8x & = &-3\\\Leftrightarrow & \color{red}{8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-x } & = & 10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+13}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13-13x } & = & -14 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &-4x & = &-27\\\Leftrightarrow & \color{red}{-4}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-27}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{27}{4} } & & \\ & V = \left\{ \frac{27}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+12}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12-8x } & = & 5 \color{red}{ +8x }\color{blue}{-12-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-10}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10+13x } & = & -10 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -10 \color{blue}{+10} \\\Leftrightarrow &20x & = &0\\\Leftrightarrow & \color{red}{20}x & = &0\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{0}{20} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-9}& = & -4 \color{red}{ +10x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9-10x } & = & -4 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & -x \color{blue}{-10x } & = & -4 \color{blue}{+9} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)