Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-10}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10-3x } & = & 9 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &8x & = &19\\\Leftrightarrow & \color{red}{8}x & = &19\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{19}{8} \\\Leftrightarrow & \color{green}{ x = \frac{19}{8} } & & \\ & V = \left\{ \frac{19}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+13}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13-5x } & = & -10 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &3x & = &-23\\\Leftrightarrow & \color{red}{3}x & = &-23\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-23}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{3} } & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x } & = & 6 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &-6x & = &17\\\Leftrightarrow & \color{red}{-6}x & = &17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{6} } & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+11}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-13x } & = & 6 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &-19x & = &-5\\\Leftrightarrow & \color{red}{-19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+12}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12-x } & = & 9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-x } & = & 3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+9}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9-3x } & = & -11 \color{red}{ +3x }\color{blue}{-9-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &7x & = &-20\\\Leftrightarrow & \color{red}{7}x & = &-20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+1}& = & 6 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1+4x } & = & 6 \color{red}{ -4x }\color{blue}{-1+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &9x & = &5\\\Leftrightarrow & \color{red}{9}x & = &5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-6}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-x } & = & 4 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &-14x & = &10\\\Leftrightarrow & \color{red}{-14}x & = &10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-9}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-x } & = & 10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &7x & = &19\\\Leftrightarrow & \color{red}{7}x & = &19\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{19}{7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &3x & = &13\\\Leftrightarrow & \color{red}{3}x & = &13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+15}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-x } & = & -12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &-9x & = &-27\\\Leftrightarrow & \color{red}{-9}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-27}{-9} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)