Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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