Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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