Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+9}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9-x } & = & 2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+7}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+2x } & = & 14 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &3x & = &7\\\Leftrightarrow & \color{red}{3}x & = &7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+14}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14+11x } & = & -6 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &17x & = &-20\\\Leftrightarrow & \color{red}{17}x & = &-20\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-20}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+4}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-7x } & = & 5 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-3}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & -14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+14}& = & -10 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14+3x } & = & -10 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &4x & = &-24\\\Leftrightarrow & \color{red}{4}x & = &-24\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-24}{4} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-11}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-5x } & = & -13 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-1}& = & -11 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1+4x } & = & -11 \color{red}{ -4x }\color{blue}{+1+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &9x & = &-10\\\Leftrightarrow & \color{red}{9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-4}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-5x } & = & 11 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & 3x \color{blue}{-5x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-2x & = &15\\\Leftrightarrow & \color{red}{-2}x & = &15\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{15}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{2} } & & \\ & V = \left\{ \frac{-15}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-x } & = & 11 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-x } & = & 3 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+8}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-5x } & = & -15 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -15 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-23\\\Leftrightarrow & \color{red}{-9}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-23}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{23}{9} } & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)