Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-x } & = & 7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+11}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11+11x } & = & -1 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &17x & = &-12\\\Leftrightarrow & \color{red}{17}x & = &-12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+9}& = & 15 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9-6x } & = & 15 \color{red}{ +6x }\color{blue}{-9-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &x & = &6\\\Leftrightarrow & \color{red}{}x & = &6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 6 \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-11}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11-5x } & = & 4 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &3x & = &15\\\Leftrightarrow & \color{red}{3}x & = &15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{15}{3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+11}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-7x } & = & -12 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-23\\\Leftrightarrow & \color{red}{-13}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-23}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-14}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-x } & = & 3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &-12x & = &17\\\Leftrightarrow & \color{red}{-12}x & = &17\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{17}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{12} } & & \\ & V = \left\{ \frac{-17}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & 15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+14}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14-7x } & = & 3 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &3x & = &-11\\\Leftrightarrow & \color{red}{3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-11}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x } & = & 15 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &-5x & = &26\\\Leftrightarrow & \color{red}{-5}x & = &26\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{26}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{5} } & & \\ & V = \left\{ \frac{-26}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-15}& = & 5 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15+13x } & = & 5 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 5 \color{blue}{+15} \\\Leftrightarrow &24x & = &20\\\Leftrightarrow & \color{red}{24}x & = &20\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{20}{24} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-x } & = & -11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-11}& = & 11 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11+7x } & = & 11 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &11x & = &22\\\Leftrightarrow & \color{red}{11}x & = &22\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{22}{11} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)