Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-10}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & 2 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &-11x & = &12\\\Leftrightarrow & \color{red}{-11}x & = &12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-2}\color{blue}{+2-x } & = & 15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &-14x & = &17\\\Leftrightarrow & \color{red}{-14}x & = &17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{14} } & & \\ & V = \left\{ \frac{-17}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x } & = & -10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-5}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x } & = & 10 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &-6x & = &15\\\Leftrightarrow & \color{red}{-6}x & = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6-x } & = & -9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -9 \color{blue}{+6} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-9}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-3x } & = & 10 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-17x & = &19\\\Leftrightarrow & \color{red}{-17}x & = &19\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{19}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{17} } & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+4}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x } & = & -15 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-19\\\Leftrightarrow & \color{red}{-11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-6}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-x } & = & 2 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+2}& = & -12 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2-15x } & = & -12 \color{red}{ +15x }\color{blue}{-2-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &-16x & = &-14\\\Leftrightarrow & \color{red}{-16}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+11}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11-5x } & = & 3 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+7}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7-7x } & = & -13 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &3x & = &-20\\\Leftrightarrow & \color{red}{3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-8}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8+13x } & = & 1 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &12x & = &9\\\Leftrightarrow & \color{red}{12}x & = &9\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{9}{12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)