Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+2}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2-5x } & = & 14 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &8x & = &12\\\Leftrightarrow & \color{red}{8}x & = &12\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{12}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+14}& = & -9 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14+2x } & = & -9 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -9 \color{blue}{-14} \\\Leftrightarrow &17x & = &-23\\\Leftrightarrow & \color{red}{17}x & = &-23\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-23}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{17} } & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-6}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6-3x } & = & 11 \color{red}{ +3x }\color{blue}{+6-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &5x & = &17\\\Leftrightarrow & \color{red}{5}x & = &17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-11}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-13x } & = & -10 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -10 \color{blue}{+11} \\\Leftrightarrow &-28x & = &1\\\Leftrightarrow & \color{red}{-28}x & = &1\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{1}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{28} } & & \\ & V = \left\{ \frac{-1}{28} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-12}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-8x } & = & 5 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &-15x & = &17\\\Leftrightarrow & \color{red}{-15}x & = &17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-x } & = & 7 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 7 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-x } & = & 7 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-3\\\Leftrightarrow & \color{red}{-6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+9}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-5x } & = & -12 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &7x & = &-21\\\Leftrightarrow & \color{red}{7}x & = &-21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-21}{7} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+13}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13-3x } & = & 15 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &2x & = &2\\\Leftrightarrow & \color{red}{2}x & = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-6}& = & -11 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6+5x } & = & -11 \color{red}{ -5x }\color{blue}{+6+5x } \\\Leftrightarrow & -x \color{blue}{+5x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &4x & = &-5\\\Leftrightarrow & \color{red}{4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9-x } & = & -2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-6x & = &-11\\\Leftrightarrow & \color{red}{-6}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-15}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & -10 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)