Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+1}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1-4x } & = & 13 \color{red}{ +4x }\color{blue}{-1-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &11x & = &12\\\Leftrightarrow & \color{red}{11}x & = &12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+4}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-3x } & = & -5 \color{red}{ +3x }\color{blue}{-4-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+10}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-x } & = & 5 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 5 \color{blue}{-10} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+2}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-9x } & = & 6 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-1}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-x } & = & 1 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+14}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14+11x } & = & -3 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &25x & = &-17\\\Leftrightarrow & \color{red}{25}x & = &-17\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-17}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{25} } & & \\ & V = \left\{ \frac{-17}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+13}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13-7x } & = & 11 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+3}& = & 10 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-12x } & = & 10 \color{red}{ +12x }\color{blue}{-3-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+8}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-13x } & = & -13 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-21\\\Leftrightarrow & \color{red}{-11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-3}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3+13x } & = & -11 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &27x & = &-8\\\Leftrightarrow & \color{red}{27}x & = &-8\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-8}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{27} } & & \\ & V = \left\{ \frac{-8}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+3}& = & 6 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-6x } & = & 6 \color{red}{ +6x }\color{blue}{-3-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 6 \color{blue}{-3} \\\Leftrightarrow &-17x & = &3\\\Leftrightarrow & \color{red}{-17}x & = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8-x } & = & 7 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 7 \color{blue}{+8} \\\Leftrightarrow &5x & = &15\\\Leftrightarrow & \color{red}{5}x & = &15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{15}{5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)