Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-5}& = & -9 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5+14x } & = & -9 \color{red}{ -14x }\color{blue}{+5+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &17x & = &-4\\\Leftrightarrow & \color{red}{17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+1}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & -14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{-1} \\\Leftrightarrow &-8x & = &-15\\\Leftrightarrow & \color{red}{-8}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-5}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-11x } & = & 5 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &-21x & = &10\\\Leftrightarrow & \color{red}{-21}x & = &10\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{10}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{21} } & & \\ & V = \left\{ \frac{-10}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-10}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10-7x } & = & 1 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 1 \color{blue}{+10} \\\Leftrightarrow &3x & = &11\\\Leftrightarrow & \color{red}{3}x & = &11\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{11}{3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-8}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8-x } & = & -6 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -6 \color{blue}{+8} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+10}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10+11x } & = & 10 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &23x & = &0\\\Leftrightarrow & \color{red}{23}x & = &0\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{0}{23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+7}& = & 4 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7-12x } & = & 4 \color{red}{ +12x }\color{blue}{-7-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &-19x & = &-3\\\Leftrightarrow & \color{red}{-19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-5}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5-x } & = & -15 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -15 \color{blue}{+5} \\\Leftrightarrow &3x & = &-10\\\Leftrightarrow & \color{red}{3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-9}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-x } & = & 7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &-10x & = &16\\\Leftrightarrow & \color{red}{-10}x & = &16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-8}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8+11x } & = & 11 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 11 \color{blue}{+8} \\\Leftrightarrow &23x & = &19\\\Leftrightarrow & \color{red}{23}x & = &19\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{19}{23} \\\Leftrightarrow & \color{green}{ x = \frac{19}{23} } & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+7}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-5x } & = & 7 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+4}& = & -12 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4+3x } & = & -12 \color{red}{ -3x }\color{blue}{-4+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &4x & = &-16\\\Leftrightarrow & \color{red}{4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-16}{4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)