Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & -2x+\frac{7}{4} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -2x+\frac{7}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{168}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-16}{ \color{blue}{8} }x+ \frac{14}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 168x \color{red}{+21} & = & \color{red}{-16x} +14 \\\Leftrightarrow & 168x \color{red}{+21} \color{blue}{-21} \color{blue}{+16x} & = & \color{red}{-16x} +14 \color{blue}{+16x} \color{blue}{-21} \\\Leftrightarrow & 168x+16x& = & 14-21 \\\Leftrightarrow & \color{red}{184} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{184} & & \\ & V = \left\{ \frac{-7}{184} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{7})& = & -5x+\frac{3}{8} \\\Leftrightarrow & 18x-\frac{30}{7}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1008}{ \color{blue}{56} }x- \frac{240}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1008x \color{red}{-240} & = & \color{red}{-280x} +21 \\\Leftrightarrow & 1008x \color{red}{-240} \color{blue}{+240} \color{blue}{+280x} & = & \color{red}{-280x} +21 \color{blue}{+280x} \color{blue}{+240} \\\Leftrightarrow & 1008x+280x& = & 21+240 \\\Leftrightarrow & \color{red}{1288} x& = & 261 \\\Leftrightarrow & x = \frac{261}{1288} & & \\ & V = \left\{ \frac{261}{1288} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-24} & = & \color{red}{50x} +3 \\\Leftrightarrow & 60x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +3 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & 60x-50x& = & 3+24 \\\Leftrightarrow & \color{red}{10} x& = & 27 \\\Leftrightarrow & x = \frac{27}{10} & & \\ & V = \left\{ \frac{27}{10} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{11})& = & -9x+\frac{7}{4} \\\Leftrightarrow & -8x+\frac{20}{11}& = & -9x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-352}{ \color{blue}{44} }x+ \frac{80}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -352x \color{red}{+80} & = & \color{red}{-396x} +77 \\\Leftrightarrow & -352x \color{red}{+80} \color{blue}{-80} \color{blue}{+396x} & = & \color{red}{-396x} +77 \color{blue}{+396x} \color{blue}{-80} \\\Leftrightarrow & -352x+396x& = & 77-80 \\\Leftrightarrow & \color{red}{44} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{44} & & \\ & V = \left\{ \frac{-3}{44} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{11})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 12x+\frac{30}{11}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x+ \frac{60}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{+60} & = & \color{red}{-110x} +77 \\\Leftrightarrow & 264x \color{red}{+60} \color{blue}{-60} \color{blue}{+110x} & = & \color{red}{-110x} +77 \color{blue}{+110x} \color{blue}{-60} \\\Leftrightarrow & 264x+110x& = & 77-60 \\\Leftrightarrow & \color{red}{374} x& = & 17 \\\Leftrightarrow & x = \frac{17}{374} & & \\\Leftrightarrow & x = \frac{1}{22} & & \\ & V = \left\{ \frac{1}{22} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x+\frac{12}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{+36} & = & \color{red}{231x} +22 \\\Leftrightarrow & -528x \color{red}{+36} \color{blue}{-36} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-36} \\\Leftrightarrow & -528x-231x& = & 22-36 \\\Leftrightarrow & \color{red}{-759} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-759} & & \\\Leftrightarrow & x = \frac{14}{759} & & \\ & V = \left\{ \frac{14}{759} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{7})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+110} & = & \color{red}{693x} +42 \\\Leftrightarrow & 770x \color{red}{+110} \color{blue}{-110} \color{blue}{-693x} & = & \color{red}{693x} +42 \color{blue}{-693x} \color{blue}{-110} \\\Leftrightarrow & 770x-693x& = & 42-110 \\\Leftrightarrow & \color{red}{77} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{77} & & \\ & V = \left\{ \frac{-68}{77} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{7})& = & 5x+\frac{5}{7} \\\Leftrightarrow & -12x+\frac{20}{7}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{+20} & = & \color{red}{35x} +5 \\\Leftrightarrow & -84x \color{red}{+20} \color{blue}{-20} \color{blue}{-35x} & = & \color{red}{35x} +5 \color{blue}{-35x} \color{blue}{-20} \\\Leftrightarrow & -84x-35x& = & 5-20 \\\Leftrightarrow & \color{red}{-119} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-119} & & \\\Leftrightarrow & x = \frac{15}{119} & & \\ & V = \left\{ \frac{15}{119} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{5})& = & -8x+\frac{7}{3} \\\Leftrightarrow & 21x+\frac{14}{5}& = & -8x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{42}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+42} & = & \color{red}{-120x} +35 \\\Leftrightarrow & 315x \color{red}{+42} \color{blue}{-42} \color{blue}{+120x} & = & \color{red}{-120x} +35 \color{blue}{+120x} \color{blue}{-42} \\\Leftrightarrow & 315x+120x& = & 35-42 \\\Leftrightarrow & \color{red}{435} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{435} & & \\ & V = \left\{ \frac{-7}{435} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{3})& = & 9x+\frac{4}{7} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 9x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+56} & = & \color{red}{189x} +12 \\\Leftrightarrow & -168x \color{red}{+56} \color{blue}{-56} \color{blue}{-189x} & = & \color{red}{189x} +12 \color{blue}{-189x} \color{blue}{-56} \\\Leftrightarrow & -168x-189x& = & 12-56 \\\Leftrightarrow & \color{red}{-357} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-357} & & \\\Leftrightarrow & x = \frac{44}{357} & & \\ & V = \left\{ \frac{44}{357} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{9})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x+\frac{20}{9}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+140} & = & \color{red}{315x} +90 \\\Leftrightarrow & -756x \color{red}{+140} \color{blue}{-140} \color{blue}{-315x} & = & \color{red}{315x} +90 \color{blue}{-315x} \color{blue}{-140} \\\Leftrightarrow & -756x-315x& = & 90-140 \\\Leftrightarrow & \color{red}{-1071} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{-1071} & & \\\Leftrightarrow & x = \frac{50}{1071} & & \\ & V = \left\{ \frac{50}{1071} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{2}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{6}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-66} & = & \color{red}{-385x} +42 \\\Leftrightarrow & 924x \color{red}{-66} \color{blue}{+66} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{+66} \\\Leftrightarrow & 924x+385x& = & 42+66 \\\Leftrightarrow & \color{red}{1309} x& = & 108 \\\Leftrightarrow & x = \frac{108}{1309} & & \\ & V = \left\{ \frac{108}{1309} \right\} & \\\end{align}\)