Vgln. eerste graad (reeks 4)

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1. \(\frac{x}{4}+\frac{2}{11}=\frac{-5}{3}x+7\)
2. \(\frac{x}{3}+\frac{3}{16}=\frac{-3}{4}x-4\)
3. \(\frac{x}{5}-\frac{5}{11}=\frac{1}{3}x+4\)
4. \(\frac{x}{4}-\frac{4}{9}=\frac{-8}{3}x-5\)
5. \(\frac{x}{3}+\frac{3}{7}=\frac{7}{2}x-3\)
6. \(\frac{x}{7}+\frac{2}{13}=\frac{1}{2}x-6\)
7. \(\frac{x}{3}-\frac{2}{7}=\frac{-3}{4}x+6\)
8. \(\frac{x}{2}-\frac{5}{16}=\frac{1}{3}x-6\)
9. \(\frac{x}{5}+\frac{4}{11}=\frac{-2}{3}x-1\)
10. \(\frac{x}{7}-\frac{5}{7}=\frac{7}{3}x-8\)
11. \(\frac{x}{7}+\frac{3}{7}=\frac{-2}{3}x-7\)
12. \(\frac{x}{6}+\frac{5}{16}=\frac{-2}{5}x-5\)

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Reeks met breuken waarbij we ervoor kiezen om de breuken weg te werken. Neem je ZRM!

Verbetersleutel

1. \(\text{132 is het kleinste gemene veelvoud van 4, 11 en 3} \\ \begin{align} & \frac{x}{4}+\frac{2}{11}& = & \frac{-5}{3}x+7 \\\Leftrightarrow & \color{blue}{132.} (\frac{33x}{ \color{blue}{132} }+ \frac{ 24 }{ \color{blue}{132} })& = & (\frac{-220}{ \color{blue}{132} }x+\frac{924}{ \color{blue}{132} }) \color{blue}{.132} \\\Leftrightarrow & 33x+24& = & -220x+924 \\\Leftrightarrow & 33x \color{red}{+24} \color{blue}{-24} \color{blue}{+220x} & = & \color{red}{-220x} +924 \color{blue}{+220x} \color{blue}{-24} \\\Leftrightarrow & 253x& = & 900 \\\Leftrightarrow & \frac{253x}{ \color{red}{253} }& = & \frac{900}{253} \\\Leftrightarrow & x = \frac{900}{253} & & \\ & V = \left\{ \frac{900}{253} \right\} & \\\end{align}\)
2. \(\text{48 is het kleinste gemene veelvoud van 3, 16 en 4} \\ \begin{align} & \frac{x}{3}+\frac{3}{16}& = & \frac{-3}{4}x-4 \\\Leftrightarrow & \color{blue}{48.} (\frac{16x}{ \color{blue}{48} }+ \frac{ 9 }{ \color{blue}{48} })& = & (\frac{-36}{ \color{blue}{48} }x-\frac{192}{ \color{blue}{48} }) \color{blue}{.48} \\\Leftrightarrow & 16x+9& = & -36x-192 \\\Leftrightarrow & 16x \color{red}{+9} \color{blue}{-9} \color{blue}{+36x} & = & \color{red}{-36x} -192 \color{blue}{+36x} \color{blue}{-9} \\\Leftrightarrow & 52x& = & -201 \\\Leftrightarrow & \frac{52x}{ \color{red}{52} }& = & \frac{-201}{52} \\\Leftrightarrow & x = \frac{-201}{52} & & \\ & V = \left\{ \frac{-201}{52} \right\} & \\\end{align}\)
3. \(\text{165 is het kleinste gemene veelvoud van 5, 11 en 3} \\ \begin{align} & \frac{x}{5}-\frac{5}{11}& = & \frac{1}{3}x+4 \\\Leftrightarrow & \color{blue}{165.} (\frac{33x}{ \color{blue}{165} }- \frac{ 75 }{ \color{blue}{165} })& = & (\frac{55}{ \color{blue}{165} }x+\frac{660}{ \color{blue}{165} }) \color{blue}{.165} \\\Leftrightarrow & 33x-75& = & 55x+660 \\\Leftrightarrow & 33x \color{red}{-75} \color{blue}{+75} \color{blue}{-55x} & = & \color{red}{55x} +660 \color{blue}{-55x} \color{blue}{+75} \\\Leftrightarrow & -22x& = & 735 \\\Leftrightarrow & \frac{-22x}{ \color{red}{-22} }& = & \frac{735}{-22} \\\Leftrightarrow & x = \frac{-735}{22} & & \\ & V = \left\{ \frac{-735}{22} \right\} & \\\end{align}\)
4. \(\text{36 is het kleinste gemene veelvoud van 4, 9 en 3} \\ \begin{align} & \frac{x}{4}-\frac{4}{9}& = & \frac{-8}{3}x-5 \\\Leftrightarrow & \color{blue}{36.} (\frac{9x}{ \color{blue}{36} }- \frac{ 16 }{ \color{blue}{36} })& = & (\frac{-96}{ \color{blue}{36} }x-\frac{180}{ \color{blue}{36} }) \color{blue}{.36} \\\Leftrightarrow & 9x-16& = & -96x-180 \\\Leftrightarrow & 9x \color{red}{-16} \color{blue}{+16} \color{blue}{+96x} & = & \color{red}{-96x} -180 \color{blue}{+96x} \color{blue}{+16} \\\Leftrightarrow & 105x& = & -164 \\\Leftrightarrow & \frac{105x}{ \color{red}{105} }& = & \frac{-164}{105} \\\Leftrightarrow & x = \frac{-164}{105} & & \\ & V = \left\{ \frac{-164}{105} \right\} & \\\end{align}\)
5. \(\text{42 is het kleinste gemene veelvoud van 3, 7 en 2} \\ \begin{align} & \frac{x}{3}+\frac{3}{7}& = & \frac{7}{2}x-3 \\\Leftrightarrow & \color{blue}{42.} (\frac{14x}{ \color{blue}{42} }+ \frac{ 18 }{ \color{blue}{42} })& = & (\frac{147}{ \color{blue}{42} }x-\frac{126}{ \color{blue}{42} }) \color{blue}{.42} \\\Leftrightarrow & 14x+18& = & 147x-126 \\\Leftrightarrow & 14x \color{red}{+18} \color{blue}{-18} \color{blue}{-147x} & = & \color{red}{147x} -126 \color{blue}{-147x} \color{blue}{-18} \\\Leftrightarrow & -133x& = & -144 \\\Leftrightarrow & \frac{-133x}{ \color{red}{-133} }& = & \frac{-144}{-133} \\\Leftrightarrow & x = \frac{144}{133} & & \\ & V = \left\{ \frac{144}{133} \right\} & \\\end{align}\)
6. \(\text{182 is het kleinste gemene veelvoud van 7, 13 en 2} \\ \begin{align} & \frac{x}{7}+\frac{2}{13}& = & \frac{1}{2}x-6 \\\Leftrightarrow & \color{blue}{182.} (\frac{26x}{ \color{blue}{182} }+ \frac{ 28 }{ \color{blue}{182} })& = & (\frac{91}{ \color{blue}{182} }x-\frac{1092}{ \color{blue}{182} }) \color{blue}{.182} \\\Leftrightarrow & 26x+28& = & 91x-1092 \\\Leftrightarrow & 26x \color{red}{+28} \color{blue}{-28} \color{blue}{-91x} & = & \color{red}{91x} -1092 \color{blue}{-91x} \color{blue}{-28} \\\Leftrightarrow & -65x& = & -1120 \\\Leftrightarrow & \frac{-65x}{ \color{red}{-65} }& = & \frac{-1120}{-65} \\\Leftrightarrow & x = \frac{224}{13} & & \\ & V = \left\{ \frac{224}{13} \right\} & \\\end{align}\)
7. \(\text{84 is het kleinste gemene veelvoud van 3, 7 en 4} \\ \begin{align} & \frac{x}{3}-\frac{2}{7}& = & \frac{-3}{4}x+6 \\\Leftrightarrow & \color{blue}{84.} (\frac{28x}{ \color{blue}{84} }- \frac{ 24 }{ \color{blue}{84} })& = & (\frac{-63}{ \color{blue}{84} }x+\frac{504}{ \color{blue}{84} }) \color{blue}{.84} \\\Leftrightarrow & 28x-24& = & -63x+504 \\\Leftrightarrow & 28x \color{red}{-24} \color{blue}{+24} \color{blue}{+63x} & = & \color{red}{-63x} +504 \color{blue}{+63x} \color{blue}{+24} \\\Leftrightarrow & 91x& = & 528 \\\Leftrightarrow & \frac{91x}{ \color{red}{91} }& = & \frac{528}{91} \\\Leftrightarrow & x = \frac{528}{91} & & \\ & V = \left\{ \frac{528}{91} \right\} & \\\end{align}\)
8. \(\text{48 is het kleinste gemene veelvoud van 2, 16 en 3} \\ \begin{align} & \frac{x}{2}-\frac{5}{16}& = & \frac{1}{3}x-6 \\\Leftrightarrow & \color{blue}{48.} (\frac{24x}{ \color{blue}{48} }- \frac{ 15 }{ \color{blue}{48} })& = & (\frac{16}{ \color{blue}{48} }x-\frac{288}{ \color{blue}{48} }) \color{blue}{.48} \\\Leftrightarrow & 24x-15& = & 16x-288 \\\Leftrightarrow & 24x \color{red}{-15} \color{blue}{+15} \color{blue}{-16x} & = & \color{red}{16x} -288 \color{blue}{-16x} \color{blue}{+15} \\\Leftrightarrow & 8x& = & -273 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = & \frac{-273}{8} \\\Leftrightarrow & x = \frac{-273}{8} & & \\ & V = \left\{ \frac{-273}{8} \right\} & \\\end{align}\)
9. \(\text{165 is het kleinste gemene veelvoud van 5, 11 en 3} \\ \begin{align} & \frac{x}{5}+\frac{4}{11}& = & \frac{-2}{3}x-1 \\\Leftrightarrow & \color{blue}{165.} (\frac{33x}{ \color{blue}{165} }+ \frac{ 60 }{ \color{blue}{165} })& = & (\frac{-110}{ \color{blue}{165} }x-\frac{165}{ \color{blue}{165} }) \color{blue}{.165} \\\Leftrightarrow & 33x+60& = & -110x-165 \\\Leftrightarrow & 33x \color{red}{+60} \color{blue}{-60} \color{blue}{+110x} & = & \color{red}{-110x} -165 \color{blue}{+110x} \color{blue}{-60} \\\Leftrightarrow & 143x& = & -225 \\\Leftrightarrow & \frac{143x}{ \color{red}{143} }& = & \frac{-225}{143} \\\Leftrightarrow & x = \frac{-225}{143} & & \\ & V = \left\{ \frac{-225}{143} \right\} & \\\end{align}\)
10. \(\text{21 is het kleinste gemene veelvoud van 7, 7 en 3} \\ \begin{align} & \frac{x}{7}-\frac{5}{7}& = & \frac{7}{3}x-8 \\\Leftrightarrow & \color{blue}{21.} (\frac{3x}{ \color{blue}{21} }- \frac{ 15 }{ \color{blue}{21} })& = & (\frac{49}{ \color{blue}{21} }x-\frac{168}{ \color{blue}{21} }) \color{blue}{.21} \\\Leftrightarrow & 3x-15& = & 49x-168 \\\Leftrightarrow & 3x \color{red}{-15} \color{blue}{+15} \color{blue}{-49x} & = & \color{red}{49x} -168 \color{blue}{-49x} \color{blue}{+15} \\\Leftrightarrow & -46x& = & -153 \\\Leftrightarrow & \frac{-46x}{ \color{red}{-46} }& = & \frac{-153}{-46} \\\Leftrightarrow & x = \frac{153}{46} & & \\ & V = \left\{ \frac{153}{46} \right\} & \\\end{align}\)
11. \(\text{21 is het kleinste gemene veelvoud van 7, 7 en 3} \\ \begin{align} & \frac{x}{7}+\frac{3}{7}& = & \frac{-2}{3}x-7 \\\Leftrightarrow & \color{blue}{21.} (\frac{3x}{ \color{blue}{21} }+ \frac{ 9 }{ \color{blue}{21} })& = & (\frac{-14}{ \color{blue}{21} }x-\frac{147}{ \color{blue}{21} }) \color{blue}{.21} \\\Leftrightarrow & 3x+9& = & -14x-147 \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{+14x} & = & \color{red}{-14x} -147 \color{blue}{+14x} \color{blue}{-9} \\\Leftrightarrow & 17x& = & -156 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = & \frac{-156}{17} \\\Leftrightarrow & x = \frac{-156}{17} & & \\ & V = \left\{ \frac{-156}{17} \right\} & \\\end{align}\)
12. \(\text{240 is het kleinste gemene veelvoud van 6, 16 en 5} \\ \begin{align} & \frac{x}{6}+\frac{5}{16}& = & \frac{-2}{5}x-5 \\\Leftrightarrow & \color{blue}{240.} (\frac{40x}{ \color{blue}{240} }+ \frac{ 75 }{ \color{blue}{240} })& = & (\frac{-96}{ \color{blue}{240} }x-\frac{1200}{ \color{blue}{240} }) \color{blue}{.240} \\\Leftrightarrow & 40x+75& = & -96x-1200 \\\Leftrightarrow & 40x \color{red}{+75} \color{blue}{-75} \color{blue}{+96x} & = & \color{red}{-96x} -1200 \color{blue}{+96x} \color{blue}{-75} \\\Leftrightarrow & 136x& = & -1275 \\\Leftrightarrow & \frac{136x}{ \color{red}{136} }& = & \frac{-1275}{136} \\\Leftrightarrow & x = \frac{-75}{8} & & \\ & V = \left\{ \frac{-75}{8} \right\} & \\\end{align}\)