Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x } & = & 9 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &x & = &23\\\Leftrightarrow & \color{red}{}x & = &23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 23 \\\Leftrightarrow & \color{green}{ x = 23 } & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-13}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13-x } & = & 3 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &3x & = &16\\\Leftrightarrow & \color{red}{3}x & = &16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-2}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-11x } & = & 6 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &-16x & = &8\\\Leftrightarrow & \color{red}{-16}x & = &8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-4}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-9x } & = & -1 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &-17x & = &3\\\Leftrightarrow & \color{red}{-17}x & = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-10}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & 14 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &-11x & = &24\\\Leftrightarrow & \color{red}{-11}x & = &24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{11} } & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+11}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-11x } & = & -4 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-12}& = & -10 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+8x } & = & -10 \color{red}{ -8x }\color{blue}{+12+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-1}& = & 15 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1+10x } & = & 15 \color{red}{ -10x }\color{blue}{+1+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &17x & = &16\\\Leftrightarrow & \color{red}{17}x & = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+14}& = & 3 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14+12x } & = & 3 \color{red}{ -12x }\color{blue}{-14+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &25x & = &-11\\\Leftrightarrow & \color{red}{25}x & = &-11\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-11}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{25} } & & \\ & V = \left\{ \frac{-11}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+10}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-11x } & = & 3 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+15}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-x } & = & 13 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-3}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-x } & = & -9 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &-8x & = &-6\\\Leftrightarrow & \color{red}{-8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)