Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+1}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-11x } & = & 6 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+11}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-x } & = & -7 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -7 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-18\\\Leftrightarrow & \color{red}{-5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-13}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13-x } & = & -2 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &6x & = &11\\\Leftrightarrow & \color{red}{6}x & = &11\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{11}{6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-9}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-7x } & = & 6 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &-16x & = &15\\\Leftrightarrow & \color{red}{-16}x & = &15\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{15}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{16} } & & \\ & V = \left\{ \frac{-15}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+2}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x } & = & 2 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 2 \color{blue}{-2} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-6}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+13x } & = & -3 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &22x & = &3\\\Leftrightarrow & \color{red}{22}x & = &3\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{3}{22} \\\Leftrightarrow & \color{green}{ x = \frac{3}{22} } & & \\ & V = \left\{ \frac{3}{22} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-x } & = & 15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &-7x & = &22\\\Leftrightarrow & \color{red}{-7}x & = &22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & -7 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-16\\\Leftrightarrow & \color{red}{-9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+3}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3-5x } & = & 2 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &3x & = &-1\\\Leftrightarrow & \color{red}{3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+4}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-7x } & = & -14 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-20x & = &-18\\\Leftrightarrow & \color{red}{-20}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-18}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+9}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & -14 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-23\\\Leftrightarrow & \color{red}{-11}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{23}{11} } & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+14}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-11x } & = & 13 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)