Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+15}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-4x } & = & -7 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &-7x & = &-22\\\Leftrightarrow & \color{red}{-7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+3}& = & 15 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3+8x } & = & 15 \color{red}{ -8x }\color{blue}{-3+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &17x & = &12\\\Leftrightarrow & \color{red}{17}x & = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-2}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2-9x } & = & 3 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-11}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-5x } & = & 2 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 2 \color{blue}{+11} \\\Leftrightarrow &-9x & = &13\\\Leftrightarrow & \color{red}{-9}x & = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-11}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+7x } & = & -2 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &6x & = &9\\\Leftrightarrow & \color{red}{6}x & = &9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-x } & = & 4 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+12}& = & -6 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+3x } & = & -6 \color{red}{ -3x }\color{blue}{-12+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &10x & = &-18\\\Leftrightarrow & \color{red}{10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-18}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-8}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-x } & = & 9 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 9 \color{blue}{+8} \\\Leftrightarrow &3x & = &17\\\Leftrightarrow & \color{red}{3}x & = &17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-3}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3+11x } & = & 7 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 7 \color{blue}{+3} \\\Leftrightarrow &23x & = &10\\\Leftrightarrow & \color{red}{23}x & = &10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-x } & = & -6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-1}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1-13x } & = & 10 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-x } & = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)