Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-9}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-3x } & = & 2 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-x } & = & -15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-12}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12+7x } & = & -15 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &12x & = &-3\\\Leftrightarrow & \color{red}{12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-3}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7-x } & = & -2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-12}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12+7x } & = & -2 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &19x & = &10\\\Leftrightarrow & \color{red}{19}x & = &10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-14}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x } & = & -10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -10 \color{blue}{+14} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-6}& = & 1 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-6}\color{blue}{+6-4x } & = & 1 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11-x } & = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &6x & = &14\\\Leftrightarrow & \color{red}{6}x & = &14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+10}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10+11x } & = & -14 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -14 \color{blue}{-10} \\\Leftrightarrow &26x & = &-24\\\Leftrightarrow & \color{red}{26}x & = &-24\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-24}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-7}& = & -1 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7+9x } & = & -1 \color{red}{ -9x }\color{blue}{+7+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -1 \color{blue}{+7} \\\Leftrightarrow &14x & = &6\\\Leftrightarrow & \color{red}{14}x & = &6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+4}& = & 4 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4+5x } & = & 4 \color{red}{ -5x }\color{blue}{-4+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-x } & = & -9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)