Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{4}{3})& = & -9x+\frac{3}{8} \\\Leftrightarrow & 25x+\frac{20}{3}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{600}{ \color{blue}{24} }x+ \frac{160}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 600x \color{red}{+160} & = & \color{red}{-216x} +9 \\\Leftrightarrow & 600x \color{red}{+160} \color{blue}{-160} \color{blue}{+216x} & = & \color{red}{-216x} +9 \color{blue}{+216x} \color{blue}{-160} \\\Leftrightarrow & 600x+216x& = & 9-160 \\\Leftrightarrow & \color{red}{816} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{816} & & \\ & V = \left\{ \frac{-151}{816} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -4x+\frac{6}{7}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{+18} & = & \color{red}{189x} +14 \\\Leftrightarrow & -84x \color{red}{+18} \color{blue}{-18} \color{blue}{-189x} & = & \color{red}{189x} +14 \color{blue}{-189x} \color{blue}{-18} \\\Leftrightarrow & -84x-189x& = & 14-18 \\\Leftrightarrow & \color{red}{-273} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-273} & & \\\Leftrightarrow & x = \frac{4}{273} & & \\ & V = \left\{ \frac{4}{273} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{7})& = & -7x+\frac{9}{5} \\\Leftrightarrow & -30x-\frac{18}{7}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x- \frac{90}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{-90} & = & \color{red}{-245x} +63 \\\Leftrightarrow & -1050x \color{red}{-90} \color{blue}{+90} \color{blue}{+245x} & = & \color{red}{-245x} +63 \color{blue}{+245x} \color{blue}{+90} \\\Leftrightarrow & -1050x+245x& = & 63+90 \\\Leftrightarrow & \color{red}{-805} x& = & 153 \\\Leftrightarrow & x = \frac{153}{-805} & & \\\Leftrightarrow & x = \frac{-153}{805} & & \\ & V = \left\{ \frac{-153}{805} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{5})& = & 5x+\frac{7}{4} \\\Leftrightarrow & -9x-\frac{9}{5}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x- \frac{36}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{100x} +35 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-100x} & = & \color{red}{100x} +35 \color{blue}{-100x} \color{blue}{+36} \\\Leftrightarrow & -180x-100x& = & 35+36 \\\Leftrightarrow & \color{red}{-280} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-280} & & \\\Leftrightarrow & x = \frac{-71}{280} & & \\ & V = \left\{ \frac{-71}{280} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{11})& = & 9x+\frac{5}{12} \\\Leftrightarrow & 14x-\frac{21}{11}& = & 9x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1848}{ \color{blue}{132} }x- \frac{252}{ \color{blue}{132} })& = & (\frac{1188}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1848x \color{red}{-252} & = & \color{red}{1188x} +55 \\\Leftrightarrow & 1848x \color{red}{-252} \color{blue}{+252} \color{blue}{-1188x} & = & \color{red}{1188x} +55 \color{blue}{-1188x} \color{blue}{+252} \\\Leftrightarrow & 1848x-1188x& = & 55+252 \\\Leftrightarrow & \color{red}{660} x& = & 307 \\\Leftrightarrow & x = \frac{307}{660} & & \\ & V = \left\{ \frac{307}{660} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{5})& = & -7x+\frac{5}{3} \\\Leftrightarrow & -10x+\frac{4}{5}& = & -7x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+12} & = & \color{red}{-105x} +25 \\\Leftrightarrow & -150x \color{red}{+12} \color{blue}{-12} \color{blue}{+105x} & = & \color{red}{-105x} +25 \color{blue}{+105x} \color{blue}{-12} \\\Leftrightarrow & -150x+105x& = & 25-12 \\\Leftrightarrow & \color{red}{-45} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-45} & & \\\Leftrightarrow & x = \frac{-13}{45} & & \\ & V = \left\{ \frac{-13}{45} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{11})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -10x-\frac{15}{11}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{105}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-105} & = & \color{red}{539x} +88 \\\Leftrightarrow & -770x \color{red}{-105} \color{blue}{+105} \color{blue}{-539x} & = & \color{red}{539x} +88 \color{blue}{-539x} \color{blue}{+105} \\\Leftrightarrow & -770x-539x& = & 88+105 \\\Leftrightarrow & \color{red}{-1309} x& = & 193 \\\Leftrightarrow & x = \frac{193}{-1309} & & \\\Leftrightarrow & x = \frac{-193}{1309} & & \\ & V = \left\{ \frac{-193}{1309} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{11})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -12x-\frac{30}{11}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x- \frac{60}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{-60} & = & \color{red}{110x} +55 \\\Leftrightarrow & -264x \color{red}{-60} \color{blue}{+60} \color{blue}{-110x} & = & \color{red}{110x} +55 \color{blue}{-110x} \color{blue}{+60} \\\Leftrightarrow & -264x-110x& = & 55+60 \\\Leftrightarrow & \color{red}{-374} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-374} & & \\\Leftrightarrow & x = \frac{-115}{374} & & \\ & V = \left\{ \frac{-115}{374} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{7})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{25}{7}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{75}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-75} & = & \color{red}{189x} +28 \\\Leftrightarrow & -420x \color{red}{-75} \color{blue}{+75} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{+75} \\\Leftrightarrow & -420x-189x& = & 28+75 \\\Leftrightarrow & \color{red}{-609} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-609} & & \\\Leftrightarrow & x = \frac{-103}{609} & & \\ & V = \left\{ \frac{-103}{609} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 30x-\frac{30}{7}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{1260}{ \color{blue}{42} }x- \frac{180}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 1260x \color{red}{-180} & = & \color{red}{-294x} +35 \\\Leftrightarrow & 1260x \color{red}{-180} \color{blue}{+180} \color{blue}{+294x} & = & \color{red}{-294x} +35 \color{blue}{+294x} \color{blue}{+180} \\\Leftrightarrow & 1260x+294x& = & 35+180 \\\Leftrightarrow & \color{red}{1554} x& = & 215 \\\Leftrightarrow & x = \frac{215}{1554} & & \\ & V = \left\{ \frac{215}{1554} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 14x+\frac{28}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{210}{ \color{blue}{15} }x+ \frac{84}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 210x \color{red}{+84} & = & \color{red}{75x} +10 \\\Leftrightarrow & 210x \color{red}{+84} \color{blue}{-84} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-84} \\\Leftrightarrow & 210x-75x& = & 10-84 \\\Leftrightarrow & \color{red}{135} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{135} & & \\ & V = \left\{ \frac{-74}{135} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{7})& = & -2x+\frac{10}{9} \\\Leftrightarrow & 25x-\frac{20}{7}& = & -2x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1575}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{-126}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1575x \color{red}{-180} & = & \color{red}{-126x} +70 \\\Leftrightarrow & 1575x \color{red}{-180} \color{blue}{+180} \color{blue}{+126x} & = & \color{red}{-126x} +70 \color{blue}{+126x} \color{blue}{+180} \\\Leftrightarrow & 1575x+126x& = & 70+180 \\\Leftrightarrow & \color{red}{1701} x& = & 250 \\\Leftrightarrow & x = \frac{250}{1701} & & \\ & V = \left\{ \frac{250}{1701} \right\} & \\\end{align}\)