Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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