Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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