Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+5}& = & 15 \color{red}{ +15x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-15x } & = & 15 \color{red}{ +15x }\color{blue}{-5-15x } \\\Leftrightarrow & -7x \color{blue}{-15x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &-22x & = &10\\\Leftrightarrow & \color{red}{-22}x & = &10\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{10}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+4}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4+11x } & = & -5 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & -15x \color{blue}{+11x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &-4x & = &-9\\\Leftrightarrow & \color{red}{-4}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-3}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-8x } & = & -10 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+1}& = & -6 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1+6x } & = & -6 \color{red}{ -6x }\color{blue}{-1+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &13x & = &-7\\\Leftrightarrow & \color{red}{13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+9}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-7x } & = & -9 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &5x & = &-18\\\Leftrightarrow & \color{red}{5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+10}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10-11x } & = & -1 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &2x & = &-11\\\Leftrightarrow & \color{red}{2}x & = &-11\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-11}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+13}& = & -5 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13-10x } & = & -5 \color{red}{ +10x }\color{blue}{-13-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-18\\\Leftrightarrow & \color{red}{-13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+2}& = & 10 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2+2x } & = & 10 \color{red}{ -2x }\color{blue}{-2+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+7}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-11x } & = & -11 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &-19x & = &-18\\\Leftrightarrow & \color{red}{-19}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-18}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{18}{19} } & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-15}& = & 10 \color{red}{ -2x } \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15+2x } & = & 10 \color{red}{ -2x }\color{blue}{+15+2x } \\\Leftrightarrow & 13x \color{blue}{+2x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &15x & = &25\\\Leftrightarrow & \color{red}{15}x & = &25\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{25}{15} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+12}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-4x } & = & -10 \color{red}{ +4x }\color{blue}{-12-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &9x & = &-22\\\Leftrightarrow & \color{red}{9}x & = &-22\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-22}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-6}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6-9x } & = & -13 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)