Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{7})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 8x+\frac{8}{7}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+24} & = & \color{red}{-105x} +56 \\\Leftrightarrow & 168x \color{red}{+24} \color{blue}{-24} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{-24} \\\Leftrightarrow & 168x+105x& = & 56-24 \\\Leftrightarrow & \color{red}{273} x& = & 32 \\\Leftrightarrow & x = \frac{32}{273} & & \\ & V = \left\{ \frac{32}{273} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & 7x+\frac{2}{7} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-168} & = & \color{red}{245x} +10 \\\Leftrightarrow & 1050x \color{red}{-168} \color{blue}{+168} \color{blue}{-245x} & = & \color{red}{245x} +10 \color{blue}{-245x} \color{blue}{+168} \\\Leftrightarrow & 1050x-245x& = & 10+168 \\\Leftrightarrow & \color{red}{805} x& = & 178 \\\Leftrightarrow & x = \frac{178}{805} & & \\ & V = \left\{ \frac{178}{805} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{11})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 6x+\frac{8}{11}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{660}{ \color{blue}{110} }x+ \frac{80}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 660x \color{red}{+80} & = & \color{red}{550x} +33 \\\Leftrightarrow & 660x \color{red}{+80} \color{blue}{-80} \color{blue}{-550x} & = & \color{red}{550x} +33 \color{blue}{-550x} \color{blue}{-80} \\\Leftrightarrow & 660x-550x& = & 33-80 \\\Leftrightarrow & \color{red}{110} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{110} & & \\ & V = \left\{ \frac{-47}{110} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{9})& = & 7x+\frac{8}{5} \\\Leftrightarrow & -10x+\frac{25}{9}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x+ \frac{125}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{+125} & = & \color{red}{315x} +72 \\\Leftrightarrow & -450x \color{red}{+125} \color{blue}{-125} \color{blue}{-315x} & = & \color{red}{315x} +72 \color{blue}{-315x} \color{blue}{-125} \\\Leftrightarrow & -450x-315x& = & 72-125 \\\Leftrightarrow & \color{red}{-765} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-765} & & \\\Leftrightarrow & x = \frac{53}{765} & & \\ & V = \left\{ \frac{53}{765} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{5}{11})& = & -5x+\frac{3}{8} \\\Leftrightarrow & 6x+\frac{15}{11}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{528}{ \color{blue}{88} }x+ \frac{120}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 528x \color{red}{+120} & = & \color{red}{-440x} +33 \\\Leftrightarrow & 528x \color{red}{+120} \color{blue}{-120} \color{blue}{+440x} & = & \color{red}{-440x} +33 \color{blue}{+440x} \color{blue}{-120} \\\Leftrightarrow & 528x+440x& = & 33-120 \\\Leftrightarrow & \color{red}{968} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{968} & & \\ & V = \left\{ \frac{-87}{968} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{252}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 252x \color{red}{+60} & = & \color{red}{70x} +21 \\\Leftrightarrow & 252x \color{red}{+60} \color{blue}{-60} \color{blue}{-70x} & = & \color{red}{70x} +21 \color{blue}{-70x} \color{blue}{-60} \\\Leftrightarrow & 252x-70x& = & 21-60 \\\Leftrightarrow & \color{red}{182} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{182} & & \\\Leftrightarrow & x = \frac{-3}{14} & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{11})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -12x-\frac{6}{11}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-6} & = & \color{red}{-55x} +10 \\\Leftrightarrow & -132x \color{red}{-6} \color{blue}{+6} \color{blue}{+55x} & = & \color{red}{-55x} +10 \color{blue}{+55x} \color{blue}{+6} \\\Leftrightarrow & -132x+55x& = & 10+6 \\\Leftrightarrow & \color{red}{-77} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-77} & & \\\Leftrightarrow & x = \frac{-16}{77} & & \\ & V = \left\{ \frac{-16}{77} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{3})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -20x-\frac{10}{3}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x- \frac{20}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{-20} & = & \color{red}{-42x} +5 \\\Leftrightarrow & -120x \color{red}{-20} \color{blue}{+20} \color{blue}{+42x} & = & \color{red}{-42x} +5 \color{blue}{+42x} \color{blue}{+20} \\\Leftrightarrow & -120x+42x& = & 5+20 \\\Leftrightarrow & \color{red}{-78} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-78} & & \\\Leftrightarrow & x = \frac{-25}{78} & & \\ & V = \left\{ \frac{-25}{78} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{4}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{24}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+24} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 60x \color{red}{+24} \color{blue}{-24} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-24} \\\Leftrightarrow & 60x+25x& = & 6-24 \\\Leftrightarrow & \color{red}{85} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{85} & & \\ & V = \left\{ \frac{-18}{85} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{11})& = & -4x+\frac{4}{3} \\\Leftrightarrow & -15x-\frac{15}{11}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x- \frac{45}{ \color{blue}{33} })& = & (\frac{-132}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{-45} & = & \color{red}{-132x} +44 \\\Leftrightarrow & -495x \color{red}{-45} \color{blue}{+45} \color{blue}{+132x} & = & \color{red}{-132x} +44 \color{blue}{+132x} \color{blue}{+45} \\\Leftrightarrow & -495x+132x& = & 44+45 \\\Leftrightarrow & \color{red}{-363} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-363} & & \\\Leftrightarrow & x = \frac{-89}{363} & & \\ & V = \left\{ \frac{-89}{363} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{5}{7})& = & -9x+\frac{2}{11} \\\Leftrightarrow & -8x-\frac{20}{7}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-220} & = & \color{red}{-693x} +14 \\\Leftrightarrow & -616x \color{red}{-220} \color{blue}{+220} \color{blue}{+693x} & = & \color{red}{-693x} +14 \color{blue}{+693x} \color{blue}{+220} \\\Leftrightarrow & -616x+693x& = & 14+220 \\\Leftrightarrow & \color{red}{77} x& = & 234 \\\Leftrightarrow & x = \frac{234}{77} & & \\ & V = \left\{ \frac{234}{77} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{9})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -4x-\frac{4}{9}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-396}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -396x \color{red}{-44} & = & \color{red}{-891x} +54 \\\Leftrightarrow & -396x \color{red}{-44} \color{blue}{+44} \color{blue}{+891x} & = & \color{red}{-891x} +54 \color{blue}{+891x} \color{blue}{+44} \\\Leftrightarrow & -396x+891x& = & 54+44 \\\Leftrightarrow & \color{red}{495} x& = & 98 \\\Leftrightarrow & x = \frac{98}{495} & & \\ & V = \left\{ \frac{98}{495} \right\} & \\\end{align}\)