Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+9}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9-5x } & = & -2 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &3x & = &-11\\\Leftrightarrow & \color{red}{3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-11}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x } & = & 4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-5\\\Leftrightarrow & \color{red}{-16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+10}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10-5x } & = & -10 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &3x & = &-20\\\Leftrightarrow & \color{red}{3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-3}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3-x } & = & -14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-x } & = & -4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-6}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-x } & = & -11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-3}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3+13x } & = & -10 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &22x & = &-7\\\Leftrightarrow & \color{red}{22}x & = &-7\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-7}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{22} } & & \\ & V = \left\{ \frac{-7}{22} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-5}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x } & = & -5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+15}& = & -6 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+8x } & = & -6 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &19x & = &-21\\\Leftrightarrow & \color{red}{19}x & = &-21\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-21}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{19} } & & \\ & V = \left\{ \frac{-21}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & -6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &-8x & = &-7\\\Leftrightarrow & \color{red}{-8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+11}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11-4x } & = & -3 \color{red}{ +4x }\color{blue}{-11-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &9x & = &-14\\\Leftrightarrow & \color{red}{9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-14}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+3}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & 5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)