Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{9})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 6x-\frac{4}{9}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{-44} & = & \color{red}{495x} +72 \\\Leftrightarrow & 594x \color{red}{-44} \color{blue}{+44} \color{blue}{-495x} & = & \color{red}{495x} +72 \color{blue}{-495x} \color{blue}{+44} \\\Leftrightarrow & 594x-495x& = & 72+44 \\\Leftrightarrow & \color{red}{99} x& = & 116 \\\Leftrightarrow & x = \frac{116}{99} & & \\ & V = \left\{ \frac{116}{99} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{4})& = & 5x+\frac{5}{8} \\\Leftrightarrow & 6x+\frac{15}{4}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{48}{ \color{blue}{8} }x+ \frac{30}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 48x \color{red}{+30} & = & \color{red}{40x} +5 \\\Leftrightarrow & 48x \color{red}{+30} \color{blue}{-30} \color{blue}{-40x} & = & \color{red}{40x} +5 \color{blue}{-40x} \color{blue}{-30} \\\Leftrightarrow & 48x-40x& = & 5-30 \\\Leftrightarrow & \color{red}{8} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{8} & & \\ & V = \left\{ \frac{-25}{8} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{3})& = & 7x+\frac{7}{5} \\\Leftrightarrow & -6x-\frac{10}{3}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x- \frac{50}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{-50} & = & \color{red}{105x} +21 \\\Leftrightarrow & -90x \color{red}{-50} \color{blue}{+50} \color{blue}{-105x} & = & \color{red}{105x} +21 \color{blue}{-105x} \color{blue}{+50} \\\Leftrightarrow & -90x-105x& = & 21+50 \\\Leftrightarrow & \color{red}{-195} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-195} & & \\\Leftrightarrow & x = \frac{-71}{195} & & \\ & V = \left\{ \frac{-71}{195} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{11})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x+\frac{30}{11}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x+ \frac{60}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{+60} & = & \color{red}{110x} +99 \\\Leftrightarrow & -264x \color{red}{+60} \color{blue}{-60} \color{blue}{-110x} & = & \color{red}{110x} +99 \color{blue}{-110x} \color{blue}{-60} \\\Leftrightarrow & -264x-110x& = & 99-60 \\\Leftrightarrow & \color{red}{-374} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-374} & & \\\Leftrightarrow & x = \frac{-39}{374} & & \\ & V = \left\{ \frac{-39}{374} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{2})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -10x-\frac{25}{2}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x- \frac{275}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{6}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{-275} & = & \color{red}{154x} +6 \\\Leftrightarrow & -220x \color{red}{-275} \color{blue}{+275} \color{blue}{-154x} & = & \color{red}{154x} +6 \color{blue}{-154x} \color{blue}{+275} \\\Leftrightarrow & -220x-154x& = & 6+275 \\\Leftrightarrow & \color{red}{-374} x& = & 281 \\\Leftrightarrow & x = \frac{281}{-374} & & \\\Leftrightarrow & x = \frac{-281}{374} & & \\ & V = \left\{ \frac{-281}{374} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{5}{6})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 10x-\frac{25}{6}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{420}{ \color{blue}{42} }x- \frac{175}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{18}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 420x \color{red}{-175} & = & \color{red}{294x} +18 \\\Leftrightarrow & 420x \color{red}{-175} \color{blue}{+175} \color{blue}{-294x} & = & \color{red}{294x} +18 \color{blue}{-294x} \color{blue}{+175} \\\Leftrightarrow & 420x-294x& = & 18+175 \\\Leftrightarrow & \color{red}{126} x& = & 193 \\\Leftrightarrow & x = \frac{193}{126} & & \\ & V = \left\{ \frac{193}{126} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{9})& = & 9x+\frac{4}{11} \\\Leftrightarrow & 35x-\frac{35}{9}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{-385} & = & \color{red}{891x} +36 \\\Leftrightarrow & 3465x \color{red}{-385} \color{blue}{+385} \color{blue}{-891x} & = & \color{red}{891x} +36 \color{blue}{-891x} \color{blue}{+385} \\\Leftrightarrow & 3465x-891x& = & 36+385 \\\Leftrightarrow & \color{red}{2574} x& = & 421 \\\Leftrightarrow & x = \frac{421}{2574} & & \\ & V = \left\{ \frac{421}{2574} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{5})& = & -7x+\frac{7}{11} \\\Leftrightarrow & -9x+\frac{12}{5}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{+132} & = & \color{red}{-385x} +35 \\\Leftrightarrow & -495x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +35 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & -495x+385x& = & 35-132 \\\Leftrightarrow & \color{red}{-110} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-110} & & \\\Leftrightarrow & x = \frac{97}{110} & & \\ & V = \left\{ \frac{97}{110} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{11})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 16x-\frac{20}{11}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{352}{ \color{blue}{22} }x- \frac{40}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 352x \color{red}{-40} & = & \color{red}{110x} +55 \\\Leftrightarrow & 352x \color{red}{-40} \color{blue}{+40} \color{blue}{-110x} & = & \color{red}{110x} +55 \color{blue}{-110x} \color{blue}{+40} \\\Leftrightarrow & 352x-110x& = & 55+40 \\\Leftrightarrow & \color{red}{242} x& = & 95 \\\Leftrightarrow & x = \frac{95}{242} & & \\ & V = \left\{ \frac{95}{242} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & 7x+\frac{7}{10} \\\Leftrightarrow & 15x+\frac{6}{7}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{+60} & = & \color{red}{490x} +49 \\\Leftrightarrow & 1050x \color{red}{+60} \color{blue}{-60} \color{blue}{-490x} & = & \color{red}{490x} +49 \color{blue}{-490x} \color{blue}{-60} \\\Leftrightarrow & 1050x-490x& = & 49-60 \\\Leftrightarrow & \color{red}{560} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{560} & & \\ & V = \left\{ \frac{-11}{560} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{7})& = & 4x+\frac{7}{12} \\\Leftrightarrow & -15x-\frac{15}{7}& = & 4x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1260}{ \color{blue}{84} }x- \frac{180}{ \color{blue}{84} })& = & (\frac{336}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1260x \color{red}{-180} & = & \color{red}{336x} +49 \\\Leftrightarrow & -1260x \color{red}{-180} \color{blue}{+180} \color{blue}{-336x} & = & \color{red}{336x} +49 \color{blue}{-336x} \color{blue}{+180} \\\Leftrightarrow & -1260x-336x& = & 49+180 \\\Leftrightarrow & \color{red}{-1596} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-1596} & & \\\Leftrightarrow & x = \frac{-229}{1596} & & \\ & V = \left\{ \frac{-229}{1596} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{2}{3})& = & -9x+\frac{5}{2} \\\Leftrightarrow & -28x+\frac{14}{3}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{+28} & = & \color{red}{-54x} +15 \\\Leftrightarrow & -168x \color{red}{+28} \color{blue}{-28} \color{blue}{+54x} & = & \color{red}{-54x} +15 \color{blue}{+54x} \color{blue}{-28} \\\Leftrightarrow & -168x+54x& = & 15-28 \\\Leftrightarrow & \color{red}{-114} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-114} & & \\\Leftrightarrow & x = \frac{13}{114} & & \\ & V = \left\{ \frac{13}{114} \right\} & \\\end{align}\)