Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{2}{3})& = & 4x+\frac{2}{5} \\\Leftrightarrow & -28x+\frac{14}{3}& = & 4x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-420}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{60}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -420x \color{red}{+70} & = & \color{red}{60x} +6 \\\Leftrightarrow & -420x \color{red}{+70} \color{blue}{-70} \color{blue}{-60x} & = & \color{red}{60x} +6 \color{blue}{-60x} \color{blue}{-70} \\\Leftrightarrow & -420x-60x& = & 6-70 \\\Leftrightarrow & \color{red}{-480} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{-480} & & \\\Leftrightarrow & x = \frac{2}{15} & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & 9x+\frac{7}{12} \\\Leftrightarrow & 20x-\frac{16}{7}& = & 9x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1680}{ \color{blue}{84} }x- \frac{192}{ \color{blue}{84} })& = & (\frac{756}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1680x \color{red}{-192} & = & \color{red}{756x} +49 \\\Leftrightarrow & 1680x \color{red}{-192} \color{blue}{+192} \color{blue}{-756x} & = & \color{red}{756x} +49 \color{blue}{-756x} \color{blue}{+192} \\\Leftrightarrow & 1680x-756x& = & 49+192 \\\Leftrightarrow & \color{red}{924} x& = & 241 \\\Leftrightarrow & x = \frac{241}{924} & & \\ & V = \left\{ \frac{241}{924} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{-54} & = & \color{red}{231x} +110 \\\Leftrightarrow & -990x \color{red}{-54} \color{blue}{+54} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+54} \\\Leftrightarrow & -990x-231x& = & 110+54 \\\Leftrightarrow & \color{red}{-1221} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-1221} & & \\\Leftrightarrow & x = \frac{-164}{1221} & & \\ & V = \left\{ \frac{-164}{1221} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 12x-\frac{15}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{75}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-75} & = & \color{red}{-245x} +28 \\\Leftrightarrow & 420x \color{red}{-75} \color{blue}{+75} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{+75} \\\Leftrightarrow & 420x+245x& = & 28+75 \\\Leftrightarrow & \color{red}{665} x& = & 103 \\\Leftrightarrow & x = \frac{103}{665} & & \\ & V = \left\{ \frac{103}{665} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{11})& = & -9x+\frac{2}{5} \\\Leftrightarrow & 14x+\frac{14}{11}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{770}{ \color{blue}{55} }x+ \frac{70}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 770x \color{red}{+70} & = & \color{red}{-495x} +22 \\\Leftrightarrow & 770x \color{red}{+70} \color{blue}{-70} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{-70} \\\Leftrightarrow & 770x+495x& = & 22-70 \\\Leftrightarrow & \color{red}{1265} x& = & -48 \\\Leftrightarrow & x = \frac{-48}{1265} & & \\ & V = \left\{ \frac{-48}{1265} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{7})& = & 7x+\frac{5}{9} \\\Leftrightarrow & -6x+\frac{15}{7}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x+ \frac{135}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{+135} & = & \color{red}{441x} +35 \\\Leftrightarrow & -378x \color{red}{+135} \color{blue}{-135} \color{blue}{-441x} & = & \color{red}{441x} +35 \color{blue}{-441x} \color{blue}{-135} \\\Leftrightarrow & -378x-441x& = & 35-135 \\\Leftrightarrow & \color{red}{-819} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{-819} & & \\\Leftrightarrow & x = \frac{100}{819} & & \\ & V = \left\{ \frac{100}{819} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{8})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 6x-\frac{15}{8}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{528}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{40}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 528x \color{red}{-165} & = & \color{red}{-440x} +40 \\\Leftrightarrow & 528x \color{red}{-165} \color{blue}{+165} \color{blue}{+440x} & = & \color{red}{-440x} +40 \color{blue}{+440x} \color{blue}{+165} \\\Leftrightarrow & 528x+440x& = & 40+165 \\\Leftrightarrow & \color{red}{968} x& = & 205 \\\Leftrightarrow & x = \frac{205}{968} & & \\ & V = \left\{ \frac{205}{968} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{5}{9})& = & 9x+\frac{9}{11} \\\Leftrightarrow & -28x-\frac{35}{9}& = & 9x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2772}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2772x \color{red}{-385} & = & \color{red}{891x} +81 \\\Leftrightarrow & -2772x \color{red}{-385} \color{blue}{+385} \color{blue}{-891x} & = & \color{red}{891x} +81 \color{blue}{-891x} \color{blue}{+385} \\\Leftrightarrow & -2772x-891x& = & 81+385 \\\Leftrightarrow & \color{red}{-3663} x& = & 466 \\\Leftrightarrow & x = \frac{466}{-3663} & & \\\Leftrightarrow & x = \frac{-466}{3663} & & \\ & V = \left\{ \frac{-466}{3663} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{9})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 10x+\frac{8}{9}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{+56} & = & \color{red}{-189x} +90 \\\Leftrightarrow & 630x \color{red}{+56} \color{blue}{-56} \color{blue}{+189x} & = & \color{red}{-189x} +90 \color{blue}{+189x} \color{blue}{-56} \\\Leftrightarrow & 630x+189x& = & 90-56 \\\Leftrightarrow & \color{red}{819} x& = & 34 \\\Leftrightarrow & x = \frac{34}{819} & & \\ & V = \left\{ \frac{34}{819} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{7})& = & 9x+\frac{6}{7} \\\Leftrightarrow & -25x+\frac{25}{7}& = & 9x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x+ \frac{25}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{+25} & = & \color{red}{63x} +6 \\\Leftrightarrow & -175x \color{red}{+25} \color{blue}{-25} \color{blue}{-63x} & = & \color{red}{63x} +6 \color{blue}{-63x} \color{blue}{-25} \\\Leftrightarrow & -175x-63x& = & 6-25 \\\Leftrightarrow & \color{red}{-238} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-238} & & \\\Leftrightarrow & x = \frac{19}{238} & & \\ & V = \left\{ \frac{19}{238} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{3})& = & 3x+\frac{9}{2} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{+16} & = & \color{red}{18x} +27 \\\Leftrightarrow & -48x \color{red}{+16} \color{blue}{-16} \color{blue}{-18x} & = & \color{red}{18x} +27 \color{blue}{-18x} \color{blue}{-16} \\\Leftrightarrow & -48x-18x& = & 27-16 \\\Leftrightarrow & \color{red}{-66} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-66} & & \\\Leftrightarrow & x = \frac{-1}{6} & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 9x+\frac{15}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x+ \frac{75}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{+75} & = & \color{red}{-245x} +28 \\\Leftrightarrow & 315x \color{red}{+75} \color{blue}{-75} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{-75} \\\Leftrightarrow & 315x+245x& = & 28-75 \\\Leftrightarrow & \color{red}{560} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{560} & & \\ & V = \left\{ \frac{-47}{560} \right\} & \\\end{align}\)