Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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