Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+4}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4-8x } & = & -8 \color{red}{ +8x }\color{blue}{-4-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-13}& = & 13 \color{red}{ +14x } \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13-14x } & = & 13 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & x \color{blue}{-14x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &-13x & = &26\\\Leftrightarrow & \color{red}{-13}x & = &26\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{26}{-13} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+3}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-11x } & = & -1 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -1 \color{blue}{-3} \\\Leftrightarrow &-21x & = &-4\\\Leftrightarrow & \color{red}{-21}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-4}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{4}{21} } & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-1}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-3x } & = & -8 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+12}& = & -9 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12+4x } & = & -9 \color{red}{ -4x }\color{blue}{-12+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &3x & = &-21\\\Leftrightarrow & \color{red}{3}x & = &-21\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-21}{3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-3}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-x } & = & 6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 6 \color{blue}{+3} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-10}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-8x } & = & -13 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &-23x & = &-3\\\Leftrightarrow & \color{red}{-23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-3}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{3}{23} } & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+6}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-11x } & = & -12 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &-19x & = &-18\\\Leftrightarrow & \color{red}{-19}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-18}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{18}{19} } & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+7}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-7x } & = & -10 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &-5x & = &-17\\\Leftrightarrow & \color{red}{-5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12-x } & = & -6 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &8x & = &-18\\\Leftrightarrow & \color{red}{8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+7}& = & -14 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+14x } & = & -14 \color{red}{ -14x }\color{blue}{-7+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &15x & = &-21\\\Leftrightarrow & \color{red}{15}x & = &-21\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-21}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)