Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-10}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-4x } & = & 7 \color{red}{ +4x }\color{blue}{+10-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+9}& = & -6 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-12x } & = & -6 \color{red}{ +12x }\color{blue}{-9-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &-23x & = &-15\\\Leftrightarrow & \color{red}{-23}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-15}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{15}{23} } & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-14}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x } & = & -13 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-5}& = & 11 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5+7x } & = & 11 \color{red}{ -7x }\color{blue}{+5+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &19x & = &16\\\Leftrightarrow & \color{red}{19}x & = &16\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{16}{19} \\\Leftrightarrow & \color{green}{ x = \frac{16}{19} } & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-14}& = & -9 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14-14x } & = & -9 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -9 \color{blue}{+14} \\\Leftrightarrow &-x & = &5\\\Leftrightarrow & \color{red}{-}x & = &5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{5}{-1} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+8}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8-10x } & = & 11 \color{red}{ +10x }\color{blue}{-8-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+15}& = & -12 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-3x } & = & -12 \color{red}{ +3x }\color{blue}{-15-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-27\\\Leftrightarrow & \color{red}{-5}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-27}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{27}{5} } & & \\ & V = \left\{ \frac{27}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4-x } & = & -10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &6x & = &-14\\\Leftrightarrow & \color{red}{6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+7}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7-x } & = & -1 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &-14x & = &-8\\\Leftrightarrow & \color{red}{-14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+1}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-14x } & = & 12 \color{red}{ +14x }\color{blue}{-1-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-23x & = &11\\\Leftrightarrow & \color{red}{-23}x & = &11\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{11}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{23} } & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-4}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-14x } & = & -5 \color{red}{ +14x }\color{blue}{+4-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+13}& = & 5 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13+3x } & = & 5 \color{red}{ -3x }\color{blue}{-13+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)