Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-50} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 350x \color{red}{-50} \color{blue}{+50} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+50} \\\Leftrightarrow & 350x+245x& = & 42+50 \\\Leftrightarrow & \color{red}{595} x& = & 92 \\\Leftrightarrow & x = \frac{92}{595} & & \\ & V = \left\{ \frac{92}{595} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & -7x+\frac{9}{5} \\\Leftrightarrow & -6x-\frac{15}{4}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{36}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{-75} & = & \color{red}{-140x} +36 \\\Leftrightarrow & -120x \color{red}{-75} \color{blue}{+75} \color{blue}{+140x} & = & \color{red}{-140x} +36 \color{blue}{+140x} \color{blue}{+75} \\\Leftrightarrow & -120x+140x& = & 36+75 \\\Leftrightarrow & \color{red}{20} x& = & 111 \\\Leftrightarrow & x = \frac{111}{20} & & \\ & V = \left\{ \frac{111}{20} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{3})& = & 3x+\frac{7}{12} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 3x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{-80} & = & \color{red}{36x} +7 \\\Leftrightarrow & 240x \color{red}{-80} \color{blue}{+80} \color{blue}{-36x} & = & \color{red}{36x} +7 \color{blue}{-36x} \color{blue}{+80} \\\Leftrightarrow & 240x-36x& = & 7+80 \\\Leftrightarrow & \color{red}{204} x& = & 87 \\\Leftrightarrow & x = \frac{87}{204} & & \\\Leftrightarrow & x = \frac{29}{68} & & \\ & V = \left\{ \frac{29}{68} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{18}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+54} & = & \color{red}{-165x} +44 \\\Leftrightarrow & -396x \color{red}{+54} \color{blue}{-54} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{-54} \\\Leftrightarrow & -396x+165x& = & 44-54 \\\Leftrightarrow & \color{red}{-231} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-231} & & \\\Leftrightarrow & x = \frac{10}{231} & & \\ & V = \left\{ \frac{10}{231} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{4})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 20x-\frac{15}{4}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{560}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 560x \color{red}{-105} & = & \color{red}{196x} +12 \\\Leftrightarrow & 560x \color{red}{-105} \color{blue}{+105} \color{blue}{-196x} & = & \color{red}{196x} +12 \color{blue}{-196x} \color{blue}{+105} \\\Leftrightarrow & 560x-196x& = & 12+105 \\\Leftrightarrow & \color{red}{364} x& = & 117 \\\Leftrightarrow & x = \frac{117}{364} & & \\\Leftrightarrow & x = \frac{9}{28} & & \\ & V = \left\{ \frac{9}{28} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{3})& = & -5x+\frac{5}{6} \\\Leftrightarrow & -4x-\frac{4}{3}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-24}{ \color{blue}{6} }x- \frac{8}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -24x \color{red}{-8} & = & \color{red}{-30x} +5 \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+30x} & = & \color{red}{-30x} +5 \color{blue}{+30x} \color{blue}{+8} \\\Leftrightarrow & -24x+30x& = & 5+8 \\\Leftrightarrow & \color{red}{6} x& = & 13 \\\Leftrightarrow & x = \frac{13}{6} & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{4})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 6x+\frac{15}{4}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{+105} & = & \color{red}{140x} +36 \\\Leftrightarrow & 168x \color{red}{+105} \color{blue}{-105} \color{blue}{-140x} & = & \color{red}{140x} +36 \color{blue}{-140x} \color{blue}{-105} \\\Leftrightarrow & 168x-140x& = & 36-105 \\\Leftrightarrow & \color{red}{28} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{28} & & \\ & V = \left\{ \frac{-69}{28} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{4}{3})& = & 6x+\frac{10}{9} \\\Leftrightarrow & 25x+\frac{20}{3}& = & 6x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{225}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{54}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 225x \color{red}{+60} & = & \color{red}{54x} +10 \\\Leftrightarrow & 225x \color{red}{+60} \color{blue}{-60} \color{blue}{-54x} & = & \color{red}{54x} +10 \color{blue}{-54x} \color{blue}{-60} \\\Leftrightarrow & 225x-54x& = & 10-60 \\\Leftrightarrow & \color{red}{171} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{171} & & \\ & V = \left\{ \frac{-50}{171} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{5})& = & 5x+\frac{4}{11} \\\Leftrightarrow & 6x+\frac{9}{5}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{+99} & = & \color{red}{275x} +20 \\\Leftrightarrow & 330x \color{red}{+99} \color{blue}{-99} \color{blue}{-275x} & = & \color{red}{275x} +20 \color{blue}{-275x} \color{blue}{-99} \\\Leftrightarrow & 330x-275x& = & 20-99 \\\Leftrightarrow & \color{red}{55} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{55} & & \\ & V = \left\{ \frac{-79}{55} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{4})& = & -9x+\frac{9}{11} \\\Leftrightarrow & 14x-\frac{35}{4}& = & -9x+\frac{9}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{616}{ \color{blue}{44} }x- \frac{385}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{36}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 616x \color{red}{-385} & = & \color{red}{-396x} +36 \\\Leftrightarrow & 616x \color{red}{-385} \color{blue}{+385} \color{blue}{+396x} & = & \color{red}{-396x} +36 \color{blue}{+396x} \color{blue}{+385} \\\Leftrightarrow & 616x+396x& = & 36+385 \\\Leftrightarrow & \color{red}{1012} x& = & 421 \\\Leftrightarrow & x = \frac{421}{1012} & & \\ & V = \left\{ \frac{421}{1012} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{3})& = & 8x+\frac{9}{10} \\\Leftrightarrow & -21x+\frac{35}{3}& = & 8x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-630}{ \color{blue}{30} }x+ \frac{350}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -630x \color{red}{+350} & = & \color{red}{240x} +27 \\\Leftrightarrow & -630x \color{red}{+350} \color{blue}{-350} \color{blue}{-240x} & = & \color{red}{240x} +27 \color{blue}{-240x} \color{blue}{-350} \\\Leftrightarrow & -630x-240x& = & 27-350 \\\Leftrightarrow & \color{red}{-870} x& = & -323 \\\Leftrightarrow & x = \frac{-323}{-870} & & \\\Leftrightarrow & x = \frac{323}{870} & & \\ & V = \left\{ \frac{323}{870} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{3})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -20x+\frac{10}{3}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{+20} & = & \color{red}{42x} +21 \\\Leftrightarrow & -120x \color{red}{+20} \color{blue}{-20} \color{blue}{-42x} & = & \color{red}{42x} +21 \color{blue}{-42x} \color{blue}{-20} \\\Leftrightarrow & -120x-42x& = & 21-20 \\\Leftrightarrow & \color{red}{-162} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-162} & & \\\Leftrightarrow & x = \frac{-1}{162} & & \\ & V = \left\{ \frac{-1}{162} \right\} & \\\end{align}\)